genuine equality, either under a federal 9+1 agreement (common president military and foreign policy) or a confederation
edit: also in case it helps; theres no baltic states, georgia, armenia or moldova in this; but transnistria and abkhazia both are. judging by what also happened irl chechnya and tatarstan would probably be member states too
probably then you would want to avoid anything recalling either Russia's triband or the SU flag. since red, green, blue and yellow are common amongst the successor states OTL, what about one of these: