As most people know, if you input a move during super flash it will come out automatically as soon as the flash is finished. However, if you perform actions for multiple moves during the flash, the move that ends up coming out is determined using a particular priority.
It appears that the game takes all of the inputs that you did during the flash and examines them. If at any point, you have a sequence of motions that would result in a super, it will come out. In addition, for each character, there is a hierarchy of which super will come out if multiple super motions were performed.
For example, Sentinel’s drones super is dominant over his puffball super, so if you did :qcb::qcf::atk::atk: or :qcf::qcb::atk::atk:, the drones super would come out in either situation.
It doesn’t matter how many motions you do in between the :d:, the :db:, the 
, and the :atk::atk:. As long as you have them sequentially in that order at some point during the freeze, the super will come out. So you could do :d::u::uf::f::s::l::f::f::db::uf::df::f:
:h::ub::u::uf::f:(:atk::atk:) and the super will still come out.
Normals, command normals, normal directional inputs (such as tapping up to jump), and X-Factor activation are not buffered during super freeze, with the exception of :s: for some reason, which is bufferable.
Dashes, super jumps, :s:, special moves, snapbacks, and supers will be buffered during super flash. Supers have the highest priority and will always come out if one is performed. But dashes, super jumps, :s:, and most special moves can be cancelled into each other and whichever one received the last input will come out.
This can be handy to know if you were going for a special move but the opponent did super in response. As long as your special move motion was performed during the super flash, you can override it with a super jump so that your special move doesn’t come out and you get super jump (where you can block) instead.
Using the partner buttons during the super flash follows a bit of a different scheme. There are three distinct actions you can take with the partner buttons: call assist, tag out, and team super. Whichever of the three you press first will come out every time. Team Super or tag out have priority over everything else (regular supers included) assuming they were the first partner action taken. If you perform a snapback, it acts like any other special move except it prevents further assist calls, unless it’s cancelled with something else.
During your own super flash
Note that this works to a certain extent during your own super flash as well as the opponent’s. However, since you are limited in what you can do after your super flash ends, there aren’t as many options.
The most obvious application is to DHC into your next character. Your next character’s input priority for their supers determines which super you’ll cancel into.
Also it seems that with certain supers which recover quickly, such as Zero’s Sougenmu (Shadow super), you can buffer special attacks during your own super freeze which will come out after the freeze is done. This is also the case with Arthur’s Golden Armor super. However it doesn’t work with Hsien-Ko’s Rimoukon (Hyper Armor super). I haven’t tested other transformation supers to see which work and which don’t.
Special Move Exceptions
There is an exception to this however. I haven’t tested every character’s special moves, but it appears that most moves performed with :s: + :atk: don’t quite follow the normal rules. It appears that most :s: + :atk: specials have priority over dashes, super jumps, and :s:, and some have priority over all other special moves as well. Here’s the breakdown that I’ve found:
The following :s: + :atk: moves can’t be directly cancelled by movement or :s:, but can be cancelled by other special moves:
Haggar - Double Lariat
M.O.D.O.K. - Body Attack
Spiderman - Web Glide
C.Viper - Focus Attack
The following :s: + :atk: moves have priority over all movement and other special moves:
Captain America - Cartwheel
Spencer - Swing Wire
Storm - Lightning Attack *can be cancelled into Flight only
Wolverine - Drill Claw
Felicia’s Foreground Dash (:s:+:atk:) doesn’t fit in with the above moves and behaves like any other special move.
What this means is that if you perform Haggar’s Lariat, if you press :d::ub: to super jump out, it won’t work and Lariat will come out instead. However, you are able to cancel Lariat into another special move, such as Violent Axe (:qcf:+:atk:) and it will come out instead of the Lariat. Taking this one step further, you can then cancel the Violent Axe into super jump in order to safely cancel the Lariat input.
For any of the :s: + :atk: moves that have multiple versions, there is also a priority between the different versions. So if you input multiple directions along with :s: + :atk:, the one with the highest priority will always come out, not necessarily the one you did last.
For directional :s: + :atk: moves, here are the priorities on the ground (1P side):
M.O.D.O.K.'s Body Attack: :ub: > > :uf: > :u: > :f:/neutral
Spencer’s Swing Wire: :uf: > :u: > :ub: > :f: > > neutral
Spiderman’s Web Glide: :u: > > :f:/neutral
Wolverine’s Drill Claw: > :ub: > :u: > :uf: > :f:/neutral
Storm’s Lightning Attack: :uf: > :u: > :ub: > :f: > > neutral
So if you perform multiple inputs of direction+:s:+:atk:, the one with the highest priority will come out no matter which order you did them in.
Input Order
If you input your directions and buttons in a non-sequential fashion, but still in the correct order overall, the move that ends with the latest input will come out (with an exception). For example, if I input :f::d::u::f:, I will get a forward dash and not a super jump since the last direction performed was an :f: and it completes a motion of a bufferable move.
It also works somewhat similarly with the button strength of a special move. So if I press :qcf::l::h:, then the medium version of the move will come out. However, there is an exception it seems. It only counts the first press after the motion is completed, so if instead I added a few buttons to the input string: :qcf::l::h::h::l:, I would still get the medium version of the move since only the first :l: and :h: after the :qcf: are counted.
The only exception to this rule that I found is snapbacks. Any additional partner button presses are ignored if it would still result in a snapback. So that means that if you press :qcf::a1::h::a2: with Ryu, you will get a :h: Hadouken since the second partner button press is ignored. However, if you completely cancel the first snapback with some other move (such as super jump) and then perform either an assist call or another snapback (with the other partner button), it will now come out.
Note that the game still allows sloppy inputs for certain moves, so :f::qcf::l: will result in a Shoryuken and not a Hadouken, even though the complete Hadouken motion was entered last. It also seems that Storm’s Whirlwind allows for some really sloppy input both normally and during super freeze. If you do :qcb::hcf::l:, it will come out as a Whirlwind (:qcb::l:) and not as a Typhoon (:qcf::l:). I’m not sure if there are other moves that are this sloppy as well.
Note that you can buffer moves during the X-Factor freeze as well and it seems to behave the same way. However, the duration of that freeze is so short that you won’t realistically be able to cancel things reliably.
General Input Priority Map
Here is a general map of move input priority during a super freeze:
[Team Super -or- Tag Out] *as long as an assist call was not made first
>
[Super 1 > Super 2 (> Super 3,4…)]
>
[certain :s:+:atk: moves]
>
[special moves = super jump = dash = :s:]
or
[certain :s:+:atk: > super jump, dash, :s:]
[certain :s:+:atk: = special moves]
[special moves = super jump = dash = :s:]
Testing Input Priority
I don’t know if people are interested, but it might be nice to get a complete input priority listing for each character. To test this out, go into training mode and pick someone like Thor as the dummy and turn input display on. Record them doing a super (such as Mighty Punish) and then during the super freeze, perform multiple direction and button inputs which would each result in a move coming out. Then see which move ends up being performed. If one move always comes out, no matter which order you perform the moves in, it has priority over the other moves you performed.
If you want to help out, please post a character’s listing using a format similar to the one I use below and I’ll edit it into this post. I’ll start off with the characters I’ve tested.
Character Priority List
Sentinel
Hyper Sentinel Force > Plasma Storm
Haggar
Final Haggar Buster (lv. 3) > Giant Haggar Press > Rapid Fire Fist
Chris
Sweep Combo > Satellite Laser (lv. 3) > Grenade Launcher
Magneto
Gravity Squeeze (lv. 3) > Magnetic Tempest > Magnetic Shockwave
Shuma-Gorath
Hyper Mystic Ray > Hyper Mystic Smash > Chaos Dimension (lv. 3)
Dr. Doom
Sphere Flame > Doom’s Time (lv. 3), > Photon Array
Jill
Mad Beast (lv. 3) > Raven Spike > Machine Gun Spray
Wesker
Lost in Nightmares (lv. 3) > Rhino Charge > Phantom Dance
Dormammu
Dark Dimension (lv. 3) > Stalking Flare > Chaotic Flame
Akuma
Raging Demon (lv. 3) > Messatsu-Goshoryu > Messatu-Gohado
Tron Bonne
Shakedown Mixer (lv. 3) > Servbot Surprise > Servbot Takeout
Zero
Genmu Zero (lv. 3) > Sougenmu > Rekkoha
Wolverine
Weapon X (lv. 3) > Berserker Charge > Fatal Claw > Berserker Barrage X
Spencer
Bionic Arm > Bionic Maneuvers
Hulk
Gamma Quake > Gamma Crush > Gamma Tsunami
Iron Man
Iron Avenger (lv. 3) > Angled Proton Cannon > Proton Cannon
Thor
Mighty Punish > Mighty Thunder > Mighty Tornado
Super Skrull
Death Penalty (lv. 3) > Inferno > Skrull Torch
(air): Inferno > Skrull Torch