Some 'flowering' varieties do produce fruit, but its often not tasty enough for us, even if edible, but can be left for the birds (Prunus padus, the bird cherry, is the obvious example). Most of the Japanese 'flowering' cultivars are sterile, and won't produce fruit, so you can assume you don't have a Japanese one, but the fact that yours is fruiting doesn't necessarily mean they're going to be edible cherries as far as you're concerned, it may still be just an ornamental tree.

Well you said this might be a daft question, so this might seem like a daft answer. All cherry trees are flowering cherry trees, if it didn't produce flowers it couldn't produce cherries and so it wouldn't be a cherry tree.

To put it another way, cherry trees that are described as flowering cherry are usually sold for the showy blooms that they produce rather than the tasty fruits. As Bamboo said, some varieties are sterile so they won't bear fruit at all.

All cherries from the Prunus family are edible, it's just that some are sweet, some are sour and there are varieties that don't really produce fruit that are worth bothering with.