You can have them be different sizes but I think the point of the flip-flop hub is not so much to be able to change cog size as to being able to switch between fixed and single speed.

I'm currently riding a fixed gear (with a flip flop hub) and have never used the single speed side. I'd think you'd get tired of changing it during your ride every day even it didn't take all that long. I would choose a cog and chainring that represents the best compromise in terms of gearing and go with that. You can certainly put a different cog on the single speed side that you might want for longer rides on hillier terrain or just when you're tired.

Remember that as young kids most of us rode single speeds everywhere using bikes that weren't particularly light and with our legs that weren't particularly strong. We managed.