Someone needs to start this. I'll give it a go and everyone can correct my stupid mistakes. Much of this information comes form this Discord, of course. This isn't meant to be fancy, just a (more) permanent record of combo work from the channel.
Empoleon's combo game is quite straightforward. There are some fancy combos he can pull off, but they rarely do as much damage as simple, boring combos. In neutral, Empoleon's combo game is very short and simple combos with strong wall carry. Empoleon's style and damage comes with his wall splat combos.
In Burst mode, the only combo path that really changes is the 2YY~Y which can finish with any HM instead of only Cut (Surf for wall carry and Rock Smash for the Defense Down). Wall combo with j.A is potentially far more dangerous in Burst Mode. Empoleon's Burst Attack sucks and is never worth more than a wall splat phase shift bonus.
AJ(1) = Aqua Jet Level 1
HM (Hidden Move) - Any button canceled from Aqua Jet
neutral (100 damage): 2YY~Y
Wall splat extension (226 damage): 2YY~B + 8A~X
This is not always a great option since it can be jumped, countered and is punishable on block, but it can be useful in scramble and stare-down situations where frames matter more than safety.
It's important to note that all parts of this combo are frame traps and not a true blockstrings! The combo engine treats 2YY as if it were a combo since AJ(1) comes out on the second Y, but an opponent can act between the 2Y and AJ(1) if they block 2Y. This means the opponent can CA your AJ or get caught mashing buttons.
Likewise, the opponent can always act between AJ(1)~Y when they block AJ(1).
Fun fact, due to scaling, you get more damage if an opponent blocks 2Y, but gets caught by the AJ after it.
In Burst mode, the AJ(1) becomes AJ(3) so it is safe on block and the AJ(3) can be hit-confirmed into any HM in neutral pushing damage to 186 on Surf or 156 on Rock Smash.
Bnb j.Y option (110 damage): j.Y + 2YY~Y
Wall splat extension (226 damage): j.Y + 2YY~B (W!) + 8A~X
Bnb j.[X] option (198 damage): j.[X]~X + 6A~A
Wall splat is the same for 228 damage
Trainimg mode suggests j.[X]~X is a true combo with correct timing. I don't know when you'd ever actually hit an opponent with j.[X], but you get a lot of damage if you do.
Wall combo only (138 damage): TK j.A (W!) + 2YY~Y
Wall splat only - low to the ground on hit (236 damage): j.A (W!) + 8Y + 8A~X
Opponent needs to be fully against the wall for this to work. Without Burst Mode, you need to hit them within a few frame of landing to combo into 8Y. In Burst Mode, enhanced Steel Wing makes the timing much more forgiving to combo into 8Y (264 damage).
Counter Attack - Crit in Neutral
BnB option, Phase Shift (139 damage): X+A crit + X + 6[A]~A
styling on a short character, max damage, Phase Shift (145 damage): X+A crit + X + 4X + 2[X]~Y~A~X
Only try the max damage when syling on a short opponent, since the incredibly tricky timing and inconsistency (AJ2 vs AJ3 randomly) is never worth the extra 6 points of damage.
Counter Attack - Crit against Wall
BnB optiion, Phase Shift (183 damage): X+A crit + 2X (W!) + 8A~X
There are fancier combos, but they all do less damage.
Okay folks. Go crazy and correct everything I got wrong and add better combos!