By Leveling Up:
* Dragon Claw: Learned at Level 20
* Sand Tomb: Learned at Level 27
* Earthquake: Learned at Level 35
* Dragon Dance: Learned at Level 44
* Outrage: Learned at Level 53
* Aerial Ace: Learned at Level 62
By TM:
* Flamethrower: TM25
* Thunderbolt: TM24
* Ice Beam: TM38
* Rock Tomb: TM39
* Earth Power: TM46
* Facade: TM47
* Aerial Ace: TM40 (Can also be learned by leveling up)
* Hidden Power: TM49
* Substitute: TM10
* Protect: TM35
* Rest: TM45
* Thief: TM48
* Double-Edge: TM34
* Ancient Power: TM37
* Swift: TM21
* Sandstorm: TM53
* Rock Slide: TM28
* Brick Break: TM50
* Iron Head: TM43
* Return: TM32
By Breeding:
* Dragon Rush: Bred from a parent who knows it.
* Dragon Pulse: Bred from a parent who knows it.
* Heat Wave: Bred from a parent who knows it.
* Mud-Slap: Bred from a parent who knows it.
* Screech: Bred from a parent who knows it.
* Tailwind: Bred from a parent who knows it.
By Move Tutor:
* Crunch: Learned at the Move Tutor in Slateport City.
* U-turn: Learned at the Move Tutor in Slateport City.
By Trade:
* Extreme Speed: Can be taught by a trainer who knows the move.
* Dragon Tail: Can be taught by a trainer who knows the move.
* Outrage: Can be taught by a trainer who knows the move (also learned by leveling up).
Note: Not all of these moves may be available in your game.
Let me know if you have any specific questions about learning moves for Flygon in Emerald!