Some people assume that plugging a phone into a car's USB charger will drain the battery. That's not really the case, certainly not in motion. When your car is running, it's the alternator that supplies power to the 12V battery that charges your phone. This adds a tiny electrical load, but it certainly won't drain your vehicle's battery flat.
When the engine isn't running, that's a slightly different matter. If your car is switched off and you charge a phone, that's going to directly draw power from the car's 12V battery. Will charging your phone for multiple hours when the engine is off flatten your car's battery? That's unlikely, though not impossible. You should avoid charging your phone in a car when the engine is off if your vehicle hasn't been driven for an extended period of time or if your car's battery is quite old.
In general, you really don't have to worry about the impact charging a phone will have on either your car's mileage or its battery. That isn't to say you should leave your phone plugged into a car's USB charger for endless hours, but when it comes to fuel or battery consumption, it's not something that should be keeping you up at night.