What are the little flaps inside my cheek?

Not medical advice: little flaps in the mouth can be caused by a few things; most likely they are fibroma, lipoma or mucosa issues.

Mucosa is that often-pink flesh that lines the mouth. A mucosa issue simply means a problem with that skin-type stuff inside your mouth. It could be an infection causing a split in the mucosa, or a tear or other kind of separation causing part of it to flap freely.

Fibroma is essentially a benign growth of connective tissue; or: extra flesh. This occurs where two surfaces of skin come together and is generally harmless.

Lipoma is like a fibroma in that it is an abnormal growth. However, a lipoma is composed of fat more than fibrous tissue and presents as smooth.

These conditions are generally more annoying than problematic, however even when the explanation is simple, the cause and treatment may not be so. As with all medical concerns: a professional should be consulted.