I have planted some hanging Tomato plants.What would cause them to keep flowering but not start to produce?

you need bees or a spray called blossom set.

Tomatoes are self-pollinating. That's not the problem. What almost certainly is is that your temperatures are too high. Not more than 100 in the daytime for most varieties. There are a number of types that do OK in heat, such as Hotset or Arkansas Traveler.

(I once had a dozen Better Boy plants going and didn't get one tomato from them. All the blossoms dropped off. I did get tomatoes from other varieties I was growing in the same location.)

They need pollinating. If you don't have any bees then you're out of luck.

BTW if you are talking about the Topsy Turvy planters, then you need to keep them thoroughly watered, too. So you should be watering them every day. They should be getting at least a pint throughout the day.