What do I do about re-seating this old flange?
Wow, that's a pretty advanced state of decay. I'll guess that the pipe is cast iron and hope the stuff you see that looks like dirt is finely crumbling bits of rusted pipe. It looks like the end of the pipe is broken away such that it would be hard to make a reliable gasket seal between the toilet and the pipe.

It's worth noting that it's always important for a toilet to be securely attached to the flange. Any amount of rocking will eventually cause a wax ring gasket to fail. If you do attempt to make this work with some kind of gaskets, having the toilet secured to the floor would be especially critical.

Since you're kind of warming up the DIY muscles... how do you feel about replacing that flooring? I'd be thinking real hard about breaking out a hole in the concrete floor. It might have to be 1-2 feet long on each side -- large enough to be able to remove the gravel or dirt beneath, cut off the failing portion of the pipe, and install new pipe, elbow, and closet flange. Finish it off with a bit of new concrete mixed in a bucket or wheelbarrow and then new flooring.