By leveling up:
* Scratch: A basic physical move that's learned early on.
* Ember: A fire-type special move that's also learned early on.
* Quick Attack: A fast physical move that's useful for getting in first.
* Flame Wheel: A powerful fire-type physical move.
* Flamethrower: A very powerful fire-type special move.
* Shadow Claw: A dark-type physical move learned at higher levels.
* Fire Blast: A very powerful fire-type special move that has a chance to burn the opponent.
* Heat Wave: A powerful fire-type special move that hits multiple targets.
* Flare Blitz: A very powerful fire-type physical move that deals a lot of damage, but also damages Flareon in the process.
* Last Resort: A powerful normal-type physical move that can only be used when the Pokémon has no other moves left.
* Sunny Day: A move that boosts the power of fire-type moves.
By TM/TR:
* Roar: A move that forces the opponent to switch out.
* Toxic: A move that poisons the opponent.
* Thunder Fang: A powerful electric-type physical move.
* Ice Fang: A powerful ice-type physical move.
* Crunch: A powerful dark-type physical move.
* Aerial Ace: A powerful flying-type physical move.
* Flame Charge: A fire-type move that raises the user's Speed stat.
* Will-O-Wisp: A move that burns the opponent.
* Protect: A move that protects the user from attacks.
* Substitute: A move that creates a substitute for the user.
* Reflect: A move that raises the user's defense stat.
* Light Screen: A move that raises the user's special defense stat.
* Safeguard: A move that prevents the user from being inflicted with status conditions.
By breeding:
* Swift: A move that always hits.
* Frustration: A move that hits harder the less the user likes its trainer.
* Return: A move that hits harder the more the user likes its trainer.
* Extremespeed: A very fast physical move.
* Quick Guard: A move that protects the user and its allies from physical attacks.
This is not an exhaustive list, but it should give you a good idea of the moves that Flareon can learn. It's important to note that the moves a Pokémon learns can vary depending on the game and its level.
Keep in mind that Flareon is a fire-type Pokémon, so it is particularly effective against grass, ice, bug, and steel types, but weak against water, rock, and ground types.