Pollination is more than likely the problem, well more of a all male flower problem. Check your flowers the females have a tiny little buds/bulbs at the base that is the beginning of the fruit. Often there will be flush of males at first. How old is your plant? Are there pollinators around? If not planting flowers that attract pollinators may not be a bad idea.
If you do have female flowers you will more than likely have males you can self pollinate them by using a small brush or q-tip or similar item to rub on the male flower stamen than deposit that on the female.
I wouldn't fear too much with time they will produce, zucchini are normally very prolific. That is if those @#$#@%#% SVB don't come around and kill them.
I hope you gave them plenty of room.