The amount of flap required varies, as does the management of the throttle. There really isn't a simple "recipe" that will work all the time.
There are a couple of definite "guidelines" though.
P51, P47, F4U, etc, vs. Spit-
-convince the spit to go fast first. The barrel roll defense is basically a means to get the guy behind you to get out in front of you (or at least get out from behind you). This is easier if he is faster than you, and/or thinks he needs to go fast to stay with you or catch you. If you're faster than him, the BRD is kind of pointless. Just fly away and get some separation. If he's the same speed as you, it can be difficult to achieve, at least in the learning stages. An easy way to get him to go fast is to put your nose down slightly, and convince him you intend to run away. He has to take this seriously, because if you can get your speed up he can't stay with you. This means he needs to catch you and shoot you NOW.
-create some closure. More is safer, less is dangerous, and it can be regulated as you master it to allow him to pass you by and then be "trapped" right in front of you for YOUR shot. This is partially where the speed of the spit comes into play. If he's catching you, he has closure. Get him fast, so he can close on you. This isn't so tough usually, because he'll have better acceleration than your P51, P47, F4U, etc... Also, he WANTS to close on you, so he can shoot you. But... if you're diving/running, how do you create closure??? You do it by turning, so he can cut across the "corner" and/or approach you from the side, rather than from directly behind. This is the part of the BRD I see most people screw up. They try to go into a barrel roll without the initial turn to the side (or up, or down, or wherever, as long as he's no longer chasing your tail...). Go right into a barrel roll, and if he's watching closely he'll just cut throttle, saddle up, and shoot you. Turn first, so that's not an easy/good option for him.
-roll around his path. Straighten out to let him approach guns range (D800- D600), and convince him to try for the shot. Just as he's getting ready to squeeze the trigger, pull up, and roll away from him. If he's coming at you from your right side, roll left. This will allow him to pass under you canopy to canopy, and then squirt out in front of you. If you've gotten him fast, and given him some closure, he won't be able to follow you through this turn/roll. He has no choice but to pass you by. Once he passes by, lots of things can happen. If he's tried to turn/roll with you, he'll be slow and sitting right in front of you. Or, he may still think he can pull this off, and try to turn with you. That'll usually put you in a rolling scissors. He may be a smart one though, and zoom up to maintain his E. That one's dangerous. Put your nose down a few degrees (avoid diving for the deck, as that leaves you out of options should he be able to catch you) and gently/smoothly turn away from him to start all over (you're back to the "convince him to go fast" part). By turning away from him, you'll maximize the turn HE needs to do to get back onto your tail, and if the separation is far enough, it'll convince him to pull that turn harder, which eats away at his E-advantage. Get him to do that 2-3 times, and he won't have that advantage anymore.
-KILL HIM QUICK. Like, RIGHT NOW. Once he's off your six, whether it's through the BRD, or the rolling scissors, you either need to kill him immediately, or extend and reset the fight. Due to his excessive speed, and inability to scrub it off quickly, you'll enjoy an advantage in turn radius BRIEFLY. Use it to kill him, or point your nose towards a safer place. If you get into a prolonged turn fight with him, you'll lose that advantage, and he'll work his way around behind you and kill you. Once again, it's about HIS speed, not just yours. He doesn't turn so well while fast.
-The flaps help you with that initial turn advantage, but again, the longer it drags out the less likely you are to survive. 2 notches or 5, it doesn't matter at that point. They help you turn, but hurt your speed. Use every bit of them that you need, but not a bit more. Retract them when you don't need, them, instead of just letting them blow back up.
-throttle plays a part. I like to back off to about 1/2 for about 1/2 second as I enter my initial turn. Then WEP for the roll. If it turns into a rolling scissors I'm generally raising and lowering my throttle with my nose (nose up, throttle up with WEP- nose down, throttle down). As the scissors drags out, and flaps come down, I'll hit a point though where I stay WEPed for the remainder of the fight.
-the helix matters. The radius of your rolls, as well as how close the rolls are matters a lot. Envision a spring stretched out, vs. one that's not stretched. The stretched out spring covers more distance forward, so that's NOT what you want to fly. Larger radius rolls, with less forward progress is what you want. Generally, that means lag pursuit, but to fine-tune it for the situation and the shot you'll need to switch between lag, pure, and lead pursuit throughout the maneuver. This is regulating closure again.
-relative E-states. The BRD plays into the disparity between your E-state and his (the spits). Having less E is a disadvantage overall, but it does create some opportunities for you that aren't immediately available for him. Use those things to your advantage, but quickly realize when the tables have turned. You'll start out disadvantaged and needing to conserve E as much as possible, but that can quickly change following the BRD or rolling scissors. Be careful not to get onto his six just to blow by HIM again...