rosie, it could be a lot of things. My first guess would be squirrels. Birds are usually good in the garden and keep the bug population down. I don't remember ever seeing birds show any interest in vegetable flowers. Strawberries maybe, but not eggplant and zucchini. If it keeps up, you could put some row covers over them, you know, that white spun fabric? Or bird netting? Good luck!

I have seen Goldfinches pull off the petals (maybe eat them too?) of certain annuals, like Sunflowers, Zinnias, and Cosmos. This probably makes it easier for them to get to the seeds. But this wouldn't apply for veggie flowers, since they are going to make veggies, and Goldfinches are seed eaters.

Since your veggie flowers are so close to the ground, perhaps it is a rodent like a squirrel or chipmunk?

Perhaps an insect is the culprit I have been told Colorado Potato Beetles will eat the blossoms off of egg plant for example.

pure speculation on my part: if the flower head/bud is actually there on the ground I'd bet on squirrel damage. Two years ago my sourwood was full of flowers? panicles? and they were all on the ground in a matter of days. Not eaten or nibbled. It could only have been squirrels.
They also dig up bulbs and leave them on the ground to mock us.
If the petals are all eaten, but the center is left, then at this time of year it could be earwigs or sometype of beetle, such as the asian beetle, "june bugs' and so on.