So I was test fitting a new holster for my Gold Cup and the hard plastic snaps caused some minor scratches
on the flat polished area of my slide. It's on the back of the slide below the rear sight.

Is there a good DIY way to re-polish that myself?

I have a dremel but I'm reluctant to go after it with the polishing wheel.

First I'd try Flitz polish.

I'd say flitz and a buffing wheel...

If you don't have a bench top buffer, you could use one of these:
Attached File

If your holster has scratched the pistol, it will do it again and again unless you cover up whatever was scratching it.  

If the marks are in fact scratches, or gouges that go into the metal, you might be able to use some contact cement to put some thin leather over what you refer to as scratches.

However, if the marks are simply deposits of brass onto the stainless steel because brass is softer than the steel, the previous suggestions of Flitz would be worth a try.  Because brass is a soft metal similar to copper, you might try using a strong copper remover such as Sweet's 7.62 bore cleaner..  Sweet's is a strong ammonia based bore cleaner that will dissolve copper and/or brass deposits in a rifle bore.  If the marks on your slide are deposits of brass rather than scratches that have cut into the stainless, Sweet's should do a great job of removing them.

I would start with Sweet's or a similar bore cleaner that is designed to dissolve copper deposits. If you polish with Flitz and a Dremel type tool before trying to dissolve what is a brass deposit rather than a scratch, you might end up with a more highly polished area on your slide that wouldn't match the rest of the slide.

Once you begin polishing a part of the slide, you run the chance of being in an endless cycle of trying to always keep the flats of the slide "pristine" and chasing after every little scratch, and brass or copper deposit.  First find out if it is a scratch or just a deposit of brass.

ETA: I re-read your initial post, and you said the plastic scratched the stainless.  There would need to be some thing harder than the stainless in order to scratch it, and steel is harder than plastic.  I suspect there was some kind of grit or dirt inside the holster that caused the scratch.

Yeah, this.  Start with the finest, least-material-removing polish you have, and only work courser if you NEED to.

Use abrasive pads with a piece of wood to keep it flat - I've taken nasty scratches out of stainless guns with this method

https://www.stewmac.com/luthier-tools-and-supplies/supplies/sanding-and-polishing/3m-scotch-brite-pads/

The gunsmith's way are the Scotchbrite polishing pads.
These are similar to the green synthetic pot scrubber pads sold in grocery stores, only in finer grit equivalents.
You can buy them online or at most automotive stores that sell car painting supplies.
White seems to match most factory finishes.

To use, "stroke" the pad in the same direction the factory grain runs.  On most auto pistols this will be front to back of the slide.
Don't just rub with the pad, that will leave circular scratches that can be hard to get out.
Don't attempt to use these pads on areas that are bead blasted, that will ruin the finish.

Never use a Dremel buff or any other small buff to try to polish a flat surface.  The small diameter wheel will just ruin the surface.
When the factory polishes metal they use very large diameter metal wheels with abrasive strips.  The larger the wheel, the easier it is to keep a surface flat.

I really liked the grit of white scotchbright.

Thanks guys.

I only test fitted that holster, didn't like it and sent it back.