I’ve been trying this out with the veg too and one book that has really helped me figure out what to use is Growing Green by Tolhurst & Hall. They have easy to read charts that detail what each cover crop does, when it can be sown, etc that has been a great tool.
I’ve tried out dwarf white clover in my kale beds and that overwintered nicely to create a good thick mat the following spring. Also tried out some winter kill cover crops like berseem clover & crimson clover, as well as oats & peas and buckwheat. Any of those would be fine planted in the time period you mentioned (buckwheat should go in earlier I think, early August). I’m aiming to move towards more winter kill cover crops so that it’s easier to deal with, not having to work it in to kill it.
Aside from whether the cover crop will come back in the spring, if you’re under sowing into an existing crop, a good thing to look at is the root structure of your flowers vs the cover crop, to make sure they aren’t competing with each other too much (ie taproot vs shallow spreading roots)