If you are printing a design that needs a white underbase can you print the white flash it and print the white again and flash and print on top of that. For example printing a logo that has white coming through it like the devil picture attached. Or would it be recommended to make 3 screens for this print

Yes, you should be able to do that but it will result in a very thick, rubbery feeling print. Normally we would create 3 screens for this doing a full white under base. The under base is printed with decent opacity but not like if we were printing white alone. Then the under base is flashed. Now you print the color on the under base and flash. After that we would print a white "highlight" screen where the white only prints again in the areas where it will be visible in the design. That way you are not building up the white under base underneath the color you want to print. The under base only needs to be decent and smooth. It does not need to be a super bright white.

The key is being able to create the white highlight screen with only the white printing on the visible white in the design. Follow?