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Guys, it'll go much faster if he uses either a 5" angle grinder, or a bench grinder! Git 'er dun!!!
Joking! Don't do that! This is a tiny job... don't use a coarse grit, and don't use anything with a motor...those will ruin it in one second. Remember, grit is the number of granules per square inch of area... so the larger the number, the more refined the grit, the smoother the finish will be.
Since this is on the slide rails though, maybe you are able to post a picture here of the offending burr? This would enable us to give better advice about just what tool is best for the lowest risk to your prized handgun.
personally I think I'd take a fine (400-600 grit or higher number) sandpaper (make sure its for metal, not wood as its a different kind of granule), and cut off a small piece maybe 1/4" square, and glue that to a popcicle stick. That way, the area being abraded is very short, even if using the slide as a guide to keep it straight.