Gyarados DB/HP FTM?

Well Bite and DB are similar in speed. I would never ever advise anyone to get rid of a legacy move especially under a circumstance such as this where it will make little difference. Keep DB, I wish I had one of those.

If you are going to use TMs on a Gyarados with Dragon Breath/Hydro Pump, you should use charge TMs to try to get Dragon Breath/Outrage.

Disagree with both. I've been calculating Cycle Damage per Second with a spreadsheet. Idea is simple, you charge up with just enough charge moves to get one full bar, then use the charged attack. Total damage divided by total time for both attacks. Some results:
Dragonite:
DT/O: 25.17
DT/H: 24.60
SW/O: 21.17
SW/H: 19.57

Hyperbeam is a little worse than Hurricane, Dragon Claw between them, and Dragon Pulse a little worse than Hyper Beam. The big difference is DT, which adds about 20% to CDPS. Dragon Breath is about 5% better than SW, still way worse than DT.

Gyarados:
B/C: 16.29
B/HP: 19.37
B/O: 18.23
DT/C: 18.79
DT/HP: 22.55
DT/O: 20.98

So Hydro Pump and Dragon Tail are the best moves to have, even without STAB for DT. Against stuff that's weak to dark, B/C is about equal to HP/DT, but B/HP is better than both.

Caveats: These numbers do include STAB, and I can build Strengths/Weaknesses into the calcs. They don't consider Attack/Defense, but that's just linear, and doesn't matter if we're comparing different moves for the same mon. They also don't consider the damage taken that turns into energy - that puts a bit more emphasis on the charged attack vs. the quick attack. And in a boss raid, one is taking a lot of damage, so it's a bigger factor yet.

YMMV, but do what you find to be the most fun.

Never.