Can you plant flowers around the base of a tree?
Growing things beneath the tree does harm them slightly. If it’s a very old or important tree or it seems stressed I would avoid it. Avoid irrigation at the base of the tree too, so you may want to avoid plants that need lots of water. Otherwise you have to decide for yourself how much you need that space. The approach many people take is to cover the area under the tree with a load of loam, then try to grow perennials in that soil. Sometimes they build a circular or geometric raised bed around the trunk of the tree to put a full 8 to 12 inches of extra soil around the tree.