JBH, you'll definitely want to hear from the more experienced voices here, but I used to have the heavy black clay when I was back in Texas. After getting a chance to speak to Dr. Church, the Collin County extension agent (who works a lot with the Noble Foundation here in OK) I learned that after numerous tests the best *permanent* fix was expanded shale and yearly additions of organic matter on top. Ok to mix compost in, but don't mix a too much mulch or wood chips (or anything heavily carbon-based) down into the soil bc it can zap all the nitrogen out of your soil and temporarily put your gardening on the sidelines. :o I've heard experience gardeners here tell of transforming their red clay into great soil with good tilth, but sounds like it took quite a while. The expanded shale however, about which you can find a lot of info on the web, is a one-time addition, and it should be mixed into the soil. There's an entire Soil Forum that discusses these kinds of questions at length, and the clay question has surely come up there. I've included a link below to the thread, but frankly I've heard better descriptions of what to do here on the Oklahoma Gardenweb. Just use the search utility or wait for one of the vets to answer.

Here is a link that might be useful: Discussion of Expanded Shale

I like compost of any kind, and then mulching with any kind of organic matter. If the beds are up next to the house, keep in mind that the insects are going to be fond of your beds also.

What kind of flowers do you want to grow? Perennials, annuals? bushes?

I really don't amend any of my flower beds. I do mulch or let the leaves self mulch in a lot of my beds.

Clay is not a bad soil despite how much we gripe about it.