I have just put in raised flower beds and I am wondering if I still need to use mulch in them?
Yes. Mulch is always helpful, even in raised beds. It helps hold moisture and keeps the groud cool.
And it will help prevent the freeze/thaw cycles that are damaging to perennials.
Raised beds need mulch more (Not more mulch) than level beds. Raised beds tend to get hotter in the summer and dry out much quicker so keep an appropriate layer of mulch on them.