Do I need locking tuners with a locking nut( Floyd)?

no, the locking nut will take care of tuning stability at the headstock end. locking tuners basically just tighten the string down, so you don't have to wind it around the tuning peg multiple times. before i had a guitar with locking tuners i had always thought they helped tuning stability, but i don't think they really do any more than standard tuners
Locking tuners, for the most part, speed up string changes.  They do help with tuning stability, especially with non-FR type tremolos.  However since you'll be using a locking nut, the tuners are taken out of the equation as soon as the locking pads are torqued down on the nut.
blue is right...not needed.  I will say my planet waves make string changing a snap compared to my gotoh 510 minis.  however...cannot beat the feel of those gotohs!!!
You will only need locking tuners if you have a nonlocking tremolo... but no matter what bridge you have locking tuners are worth considering because it is much easier to change strings.