97 Chevy cavalier

when my car is idling i have heat but takes forever to heat up…but when i drive i get no heat at all the temperature falls and it stays cold the heater blows cold air not hot…we are thinking just a flush of the system but not sure can anyone help???

That really will not solve your problem. If I am correct, your heater ducting is contrled my vacuum, and that is where you problem is. I suggest you look under the hood and see if there is a round ball with two small hoses comming out of it. If it does have, that part is the problem. If not, you will have to take it to a mechanic to find the leak.

Flushing will not help. If that were the problem you would get the heat when driving. The problem is almost certainly a vacuum issue. Somewhere you likely have a vacuum hose that is cracked or loose. This could be more important than you think because the vacuum likely also provides power assist to your brakes. You don’t want trouble there.

If you are mechanically inclined, you can start following vacuum hoses and listening for hissing leaks or disconnected/kinked hoses.  As wizard suggested one or more ball things with hoses attached also could be part of the vacuum system.  You may even have a map of where the hoses are under the hood someplace. 

Good luck

The thermostat may be stuck open, or, someone may have removed it in the mistaken belief that removing the thermostat will yield more heat in the cabin.
The radiator fan may be running when the engine is cold. That’s easy to find out. Just open the hood and see if the fan is running.

The brakes are new and work fine. When I was looking I didn’t see are hear anything out of the ordinary.

Would it help if I flush out the heater core?

Only if the heater core is plugged.