I start up Diablo (not Diablo Classic) and the screen regularly flickers, like it readjusts or something because I can see my desktop for a split second when that happens.

I noticed that if I set the resolution to "set by application" in the video settings the launcher provides, the flickering stops, but obviously the resolution is very low and it stretches the image.

I wanted to know if anyone's got a solution for this, as I want to play this as vanilla as possible (don't tell me to use a source port, as I stated, I want to play this as is)

Use Windows 95

,,, or configure your GPU to handle the upscaling and aspect ratio. Some monitors may also have such options but I'm guessing yours does not.

you could possibly run the executable directly, rather than using the gog launcher. at least that works for me. though it limits your resolution. the game still runs with black bars on the sides even with fullhd and it gives you nothing extra. i do not have this problem myself so, it could a local incompatibility with your gpu. if you posted your dxdiag, i could check.