If it's magnetic you can weld to it. Flux core is too general to tell you if you have the right wire, not all flux core is the same. Fluxcore just means the shielding gas is inside the wire or rod rather than the bottle. Is it a MIG machine or stick? You can weld stainless, but not a with a MIG welder as far as I know.
As long as you're welding steel (not stainless) it should be just fine. Most wire that you pick up at a Lowes, Home Depot, ect is going to be general purpose. Just make sure everything is extremely clean before you go welding with flux core.
And I don't mean for this to come across as offensive, but given that you had to ask basic questions about whether or not you could use your machine and wire I'd assume you don't really have the skill to do the welding you need to do. Like Tim suggested, you're probably better off having a muffler shop do it. It'll cost you a lot less than if you do it wrong and there's a lot of ways for it to go wrong.