Flour is an item in Bread Kittens used for baking various kinds of bread. It is usually obtained as a reward after battle, but completing some achievements will reward you with flour as well. Flour can also be bought with Meowbux. The Daily Spin will also get you flour. And it's common in the Spin. Trust me, I know from experience.
Baking is a key function in Bread Kittens. By baking, the player can get capture bread as well as equipment bread. Flour is used as the "price" for baking, with the amount spent depending on the bread being baked. However, the player will have to wait a given amount of time as well as the flour price.
By battling other cats, you can earn flour as well as other materials, such as Cat Chow. Battling -- and defeating -- cats of higher levels than your team usually results in a higher reward.