I have a 1986 ford mustang GT I have just replaced the starter and ran for a few days. Now the car wont start up again. Could it be the starter or the fly wheel that went bad?

take the starter off and have it bench tested, sometimes, especially rebuilts are faulty. check the teeth on the starter ring while you have it off. is it locking up when you turn the key? what are the symptoms?

Is the starter spinning the engine over when you turn the key?
What typt of sound does it make when you attempt to start the engine?

it is not locking up when you turn the key. the starter just spins. manually turn the motor the car starts. The same kind of sound when you bench test.

(Quote)Now the car wont start up again.

Not enough detail. Like saying "Number One New York".

When you turn the ignition key does the engine crank?

or

Is the engine not even cranking?

if starter ring good you may have to many shims / spacers on the engine to starter connection

No "Shims" on a Ford Jerry. Most likely problem is that it was rebuilt by "Stevie Wonder". You know the "dance" with rebuilt parts. Frequently have to go through 20 rebuilts before hitting one one good one.

Have starter checked at a place like autozone (for free). While it's out (or even before, for that matter) turn the engine by hand to check the flywheel for bad teeth. since it cranks after you turn the engine by hand, it's probably a bad flywheel, 'cause what you're doing is turning the bad spot away from the starter and then it engages the good teeth of the flywheel--and startes.

If flywheel teeth are bad, check starter pinion gear as well.

sounds like you have a problem other than the starter, have the starter tested outside of the car and check electrical system with starter out to make sure it doesnt short out your new starter.

check for corrosion in the starter solinoid connector that goes to the flat term. on starter, verry common