is radiator flushing safe

If there's a rusty sludge kind of thing going on it should be replaced . Of course if you want you can waste your time flushing it a bunch of times to see for yourself . The car's pretty old are you sure it's rusty sludge ? Are you sure it's worth it ? Could it be oil from a blown head gasket ?

No it's definitely not oil or head gasket?

Most likely it needs replaced, but if you are going to try flushing it make sure you use the right flushing solvent and nuetrialiser for the vehicle, then refill with the proper mix off antifreeze for your area. Note: if it does start leaking afterwards do NOT use any kind of stop leak as it will plug up smaller water passages in the engine and really cause a problem.

In a twenty-two year old Cavalier, I'm surprised the radiator isn't all rust. And It might just be the sludge that's holding it together. The car's not worth much, but if you intend to rely on it, it's worth replacing that radiator and not risking all that gunk getting spread throughout the cooling and interior heating system..... Why do people with old, crap cars continually cheapen out on maintenance? Treat the car right and the car will treat you right.

Check ebay for a new radiator. I found brand new radiators for my 2000 Grand Prix and 2003 S10 Pick Up for around $85 each on ebay. They both fit and work fine. The Grand Prix radiator I bought in 2016 and the S10 radiator earlier this year. I'd flush the system first then put your new radiator in. That way none of the junk from the cooling system will get into your new radiator. Hope that helps! Jim