From RWP Wiki
Red Feathers are items that first appeared in Banjo-Kazooie, in the appearance of a a simple red feather swaying gently from some unknown breeze. Red feathers are needed when you want to flap higher while flying(You need to use a flying pad to fly) or when you want to do the beak-bomb move while flying. Foe each flap or beak-bomb you do, your red feather count will decrease by one. Red feathers are limited in BK, but they always refresh when you leave that level.
Red feathers return to Banjo-Tooie for the same purpose, only this time, red feathers are unlimited and appear in a nest which switches from Gold Feather to red feathers every few seconds, grabbing the nest while it's showing red feathers will give you a couple red feathers, the same goes when it's showing golden feathers, except it'll give you a few golden feathers. In BT, a new move you can learn from Jamjars is called the Kazooie Torpedo which only works underwater, which allowed you to take Kazooie out to be used as a torpedo to destroy underwater Kazooie doors and Kazooie switches. Performing a Kazooie torpedo will decrease a few of your red feathers.
Red feathers did not appear in Banjo-Kazooie: Grunty's Revenge because there was no option to fly around in this GBA game. Red feathers also didn't appear in Banjo-Pilot due to it was unneeded in an airplane racing game.
BK's max red feather count is 50, but if you can find Cheato then one of the cheats he'll give you is "Redfeathers" which will raise the max number to 100. Similarly, BT's is 100, but if you collect enough cheato pages for Cheato, you can then enter "feathers" in code chamber to raise the red feather count to 200 and the gold feather count from 10 to 20. In the code chamber room, you can also enter "Cheato" and then "Nestking" to make your red feather and gold feather count unlimited.