Can Flesh flies Harm Or Kill me or my cats? Please Help! EMERGENCY!?

I just had my first encounter with flesh flies. The Ones That I found In my house are Long And green and black army spots on the body, red eyes, and a red orange bubble on the ***..I don't know how they are getting . they just keep appearing no matter how many i kill.. My complex is doing poisoned food boxes for mice right now.. so I know that's where they are spawning from. Just don't know where the dead mice are but obviously it is somewhere around my place. When I kill the them after a while more will appear and they make this weird screech when they die. my cats have been extremely enticed. Not knowing that these flies are harmful. I let the cats play with the flies and they chewed them up. After noticing that the number of flies is going up. i decided to look up these flies. finding out their name , I am worried that they can harm my cats. Please help me :( I need to know if my cats are sick..anything any information is appreciated