Personally I refrain from using speedbrakes against flaps. Speedbrakes for me come out at high speed only. Once Flaps are out I just stay high on profile and drop the gear a few miles earlier. That aside I don't know what the maximum obtainable rate of descent is with just speedbrakes out. I would say that if you bring it back to Clean speed and then just drop the nose you can reach a maximum ROD at -10° BA. Go beyond that and technically you are in an airplane upset condition. Your last option then is to sideslip it manually. But expect a few dozen sick passengers and start updating your CV
