Here's a breakdown of the moves Combusken learns by leveling up:
Level Up:
* Level 1: Scratch, Growl
* Level 4: Ember
* Level 7: Quick Attack
* Level 10: Flame Wheel
* Level 13: Peck
* Level 16: Swift
* Level 19: Double-Edge
* Level 22: Sky Uppercut
* Level 25: Blaze Kick
* Level 28: Aerial Ace
* Level 31: Brave Bird
* Level 34: Flare Blitz
* Level 37: Nasty Plot
* Level 40: Close Combat
* Level 43: Acrobatics
* Level 46: Heat Wave
* Level 49: Overheat
* Level 52: Superpower
* Level 55: U-turn
* Level 58: Aura Sphere
TM/HM:
Combusken can also learn various moves through Technical Machines (TM) and Hidden Machines (HM):
* TM01: Focus Blast
* TM05: Roar
* TM06: Toxic
* TM10: Hidden Power
* TM11: Sunny Day
* TM12: Taunt
* TM17: Protect
* TM18: Rain Dance
* TM21: Dazzling Gleam
* TM22: Solar Beam
* TM24: Thunderbolt
* TM27: Return
* TM28: Dig
* TM29: Psychic
* TM30: Shadow Claw
* TM31: Brick Break
* TM32: Double Team
* TM39: Rock Tomb
* TM40: Aerial Ace
* TM42: Facade
* TM44: Rest
* TM45: Attract
* TM48: Skill Swap
* TM49: Snore
* TM50: Overheat
* TM51: Roost
* TM52: Focus Blast
* TM55: Scald
* TM60: Quick Guard
* TM68: Giga Impact
* TM70: Flash Cannon
* TM76: Stealth Rock
* TM80: Rock Slide
* TM87: Swagger
* TM90: Substitute
* TM94: Surf
* TM99: Reflect
* TM100: Thunder Wave
* HM01: Cut
* HM04: Strength
* HM05: Flash
* HM06: Rock Smash
* HM07: Waterfall
* HM08: Dive
Breeding:
Combusken can learn moves through breeding with other Pokémon. This allows it to inherit moves from its parents, even if it doesn't learn those moves by leveling up.
Note: This list is not exhaustive and may be subject to change in different generations.