Rudder trim would be very important where the thrust is so dramatically asymmetric. Even small single-engine planes often have a trim tab on the rudder, but it’s fixed in place by an engineer and the pilot doesn’t touch it. But multi-engine planes have rudder trim that is adjustable in flight.
I’m not sure if you’re joking about “tail flaps”, but those movable control surfaces at the back of the plane are the elevators. Flaps are extensions of the wing that increase lift and drag (they’ll allow you to climb and descend more steeply). Flaps and elevators are always symmetric if they are operating correctly.
The A-10 Thunderbolt’s main gun’s firing cylinder being centered has more to do with keeping the nose (and gun) on target than avoiding a spin, it would need to be quite a bit outboard of center to cause the aircraft to lose control.