A proverb here and a chance to improve your bird vocabulary!
The fluffy bits on a bird that help it to fly are feathers. The phrase 'of a feather' means of the same type.
Flock is a collective noun for birds although it can also be for sheep!
So as a verb, it means to stay together. Therefore, the whole idiom means that people of a similar type stay together - simple!
Two video clips today - first, Birds of a Feather - a popular TV comedy from the eighties. Quite strong London accents in this. Then just for fun, a group with the unlikely name of A Flock of Seagulls - 80's electropop, check out the hair styles!