Depending on how high your scope sits, you probably won’t be able to screw a sunshade on and off with a flip up cap on it. I have Vortex defender caps on an ATACR (heresy, I know) in 1.50” rings and the sunshade won’t turn because of the hinge on the flip cap. So you’ll probably have to take the cap off anyway.
Edit cause I think I misunderstood your question. I mount the flip up caps on the scope then if I use the shade I put the cap on it. The shade will be the same outer diameter as the rest of the objective bell so just take off the cap, screw on sunshade, replace the cap on the shade.