There's more than one way to skin a cat. All of the combinations you mentioned can be done. Which one is best is determined by the specifics of each job.
For example, using your red/white image, I would look at the length of the run. If it was short (a few dozen), I'd probably use 2 screens: white-flash-white-flash-red. I'd probably use 200 mesh for white, 156 for red. Reason = the extra flash doesn't waste as much time as the prep/setup/teardown/reclaim of a 3rd screen. But that's only if I think the printed results will be satisfactory this way when considering the subtrate material, inks used, and specific artwork. In general, the way Mooseman described it is better: base white, flash, red, white.
As for when to flash vs when to print wet on wet, it depends largely on the ink and the design. Not what you asked about, but simulated process & true process are intentionally printed WOW - and the inks used are formulated accordingly, and the designs are created/sepped accordingly. But with spot color, that isn't always the case. The simple answer is: as often as you can get away with it, don't flash between colors; but sometimes its necessary*. Certain butt-registered colors may get muddy where they meet if you don't. (In my experience, yellow is particularly susceptible to this.) Or, your design may include large filled areas which will cause the shirt to stick to the next screen & lift if you don't flash.
(*You may see it argued that flashing between colors shouldn't be necessary if you've got all of your printing parameters precisely dialed in. Perhaps that's technically true. But practically speaking, many of us aren't working with ideal equipment or perfect technique, and flashing is sometimes part of getting the job done.)
As for flashing temp, I don't have a spec. "Gelled, not fully cured" is the rule of thumb. If it is wet to the touch, flash longer; if it is so dry that you can't smudge it even if you try, back of a little. Other folks may have more precise advice!
