The pull chain broke off and I want to put a new chain in, but there are these weird boltsI can't get off. They don't have places to put in any type of screwdriver, the head of the screw is just smooth, and the ends are flared. I have no idea how to take them off.

What you describe sounds like rivets. Apparently switch is not intend to be disassembled. No serviceable parts inside. Only way to disassemble is to drill out the flared end of rivets. If you get it apart you probably won't be able to reassemble it.