The book of simple music I've been using for piano sight reading practice has really helped me deeply memorize key signatures. However it seems most of the keys with flats in them were neglected. I'd like to get more comfortable with all major keys before moving on. Is there any good source (free if possible) of simple piano sheet music that covers every key?
Try Schubert's various dances for piano. This is the best source I can think of to answer your question. They are easy enough for sight reading - very numerous so you will have a lot to work through - and they are available for free at IMSLP. (But, the Dover edition isn't too expensive.)
Another thing to try is sight read from a hymnal. I know this is not specifically piano music, but the simple vocal lines are good for reading, there are usually hundreds of pieces in a book, and a variety of keys can be found. You many need to explore a few to find the right mix of material. I picked up a few at thrift stores on the cheap.