I've looked over the flags, and here's my educated guess about what they do, in order from least significant (far right) flag to most significant (far left) flag:
1. This move makes physical contact with the target.
2. This is a two-turn attack that hits on the second turn (like Fly).
3. This is a two-turn attack that hits of the first turn (like Hyper Beam).
4. This move is blocked by Protect and Detect.
5. This move is reflected by Magic Coat.
6. This move can be stolen by Snatch.
7. This move is replicable by Mirror Move.
8. This move is boosted by Iron Fist.
9. This is a sound-based move (blocked by Soundproof).
10. This move cannot be used during Gravity.
11. This move is usable by a frozen Pokémon. (This may always thaw the user, I have no idea. Boiling Water and Cross Fire have it along with Flare Blitz, Flame Wheel, and Sacred Fire)
12. This one has me stumped. Most (if not all) Flying-type attacks have it, along with 'pulse' attacks, like Water Pulse, Healing Pulse, Aura Sphere, etc. Maybe these are boosted by an effect now? *Keeps fingers crossed for Tailwind*
13. This move cannot be used if the user has the Heal Block effect.
14. This is the list that coyotte posted. If I had to hazard a guess, I'd say that these moves all go through Substitute now. Could somebody test this?
15 and 16. Glancing through the list quickly, these seem to be unused. It's possible I missed a move, though.