 This phase I trial is studying the side effects and best dose of alvocidib in treating patients with locally advanced or metastatic solid tumors. Drugs used in chemotherapy, such as alvocidib, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Alvocidib may also stimulate the immune system in different ways and stop tumor cells from growing. It may also stop the growth of solid tumors by blocking blood flow to the tumor. 