Suddenly my car makes a sound like a flat rear tire at low speeds (0-15 mph). the tires are fine.

A noise like that from the rear could be from the rear differential bearings or wheel bearings. Also , tires can be slightly elusive about noises, I wouldn't rule out tires until proven ok. Street Tech Auto Care can look into for you anytime. Even if you dont have us fix it, you will at least know what is wrong. Please do call or come by.