Do I need to put a second layer of damp proof membrane under my laminate flooring?
Concrete wicks water, so even if the membrane under your screed layer is undamaged, if any moisture gets into that layer it's going to be redistributed as evenly as possible throughout that layer.

What you don't want to do, with a DPM under the screed, is create a moisture trap - which a second DPM would do.

Instead of a membrane, use a foam underlayment material which will keep the wood from touching the screed directly (avoiding any moisture transfer) but which will also allow the screed to breathe and thus dry over time.