Do I have to replace the thermostat when doing a coolant flush

You do not have to change it but it is a good idea to do so while you already have the system drained. On the Corsica the exhaust crossover is over it and the throttle body is in the way as well. Normally I will remove the crossover pipe then use a bent wrench to remove the top bolt. If it was my vehicle I would remove the throttle body as well, that would enable you to clean the carbon and dirt out of it as well, plus gives you better access.