I’ve witnessed the damage a chain stay mounted kickstand can do. In this case, the damage was caused by the kickstand clamp twisting on the stay, scraping the paint and aluminum. The owner decided that the solution was to clamp the kickstand down even tighter, crushing the stay. A similar problem exists with the type that clamp behind the bottom bracket; crushed chain stays.

There is a chain stay kickstand option that clamps to both the chain stay and the seat stay. Rotational forces are countered with two mounting points, eliminating the need for excessive torque on the chain stay. If the kickstand doesn’t include some type of rubber frame protection, I’d add a thin strip or maybe a piece of discarded hose.