The soil is going to be quite dry under the trees, so annual flowers that you replant each year is out of the question. You need perennial types where the same plant returns year after year. Any of the epimediums would be a good choice. Epimedium x rubrum will be the easiest. Orangekönigin epimedium is also easy and spreads 4-6 inches a year, although it is not a prolific producer of flowers (for me, at least). Hepatica ought to do nicely, too. Since the soil is predominantly dry because of the trees' roots, don't expect anything to grow quickly. They will need to compete with the roots already there, and adapt.