Phoenixes are from the mod Exotic Birds and do not naturally spawn in the wild. You may find Phoenix Dust as loot in Dungeons and Towers. Right clicking a phoenix with a saddle will put a saddle on it, after which you can ride it.
To get a phoenix you'll need to hatch a phoenix egg. To do this you'll need to surround an egg with Phoenix Dust in a crafting table to get a phoenix egg.
Once you have this phoenix egg you'll need to place it in an area with a light level of at least 9. You'll know you're at a high enough light level if the egg gives off flame particles.
There are 8 different types of phoenixes that all require to be hatched for 2 Minecraft Days (40 Real Life minutes) in a loaded chunk. [Breaking the Egg resets the timer]
Black Phoenix:
- Hatch the egg during a full moon
- Takes damage from water
Cloud Phoenix:
- Hatch the egg above the clouds. (Over y 128)
- Immune to water damage
Desert Phoenix:
- Hatch the egg in a desert biome
- Takes damage from water
Ender Phoenix:
- Hatch the egg in the End
- Takes damage in water and will teleport when it comes in contact with it
Nether Phoenix:
- Hatch the egg in the Nether
- Immune to Fire Damage
Snow Phoenix:
- Hatch the egg in a snowy biome
- It takes damage in warm biomes (Jungle, Deserts, etc)
Water Phoenix:
- Hatch the egg in an ocean biome
- Immune to water damage
Regular Phoenix:
- Will hatch if none of the other phoenix requirements are met
- Takes damage from water
