reverse is gone after it warms up fine when cold

How many miles does your Ford have on it? If the vehicle has a lot miles, sometimes it is not a good idea to flush out the trans. It is important to use the correct fluid, many of the later Fords use a Mercon5 Synthetic fluid. It sounds like there is a temperature problem with the High/Reverse clutch which is usually the first to wear in a Ford Auto trans. ( I used to rebuild Ford tranny's in Ford Dealerships). Let me know about these questions.