Hi @TheFaculty
I don’t want to discourage you but trying to chase parity viewing on all systems is a fools game. Especially when you are dealing with colour managed and non colour managed programes. You mention frame.io but that could look one way on chrome and another on safari or firefox.
I can direct you to another post with my musings on this topic: sRGB Encoding vs Gamma 2.2 - #2 by PlaceYourBetts
And there are a few excellent posts from @finnjaeger Plus this - Quicktime Color Management: why so many ISSUES?!
Are you sending R3D to Flame from Resolve? Can I suggest ProRes 4444 or 4444XQ rather than 422HQ. About Apple ProRes - Apple Support.
You are going to be grading log and you will preserve more information (10-bit vs 12-bit) in a 4444 XQ than you will in 422HQ although log is incredibly versatile.