Flodström was born in Söderhamn, Sweden. He studied engineering physics and electrical engineering in Linköping. In 1975, he was awarded a Ph.D. in physics in Linköping with the thesis "Electronic structure of clean and oxygen covered aluminium and magnesium surfaces studied by photoelectron spectroscopy ". Flodström was also one of the initiators of the synchrotron facility MAX-Lab in Lund, where he served as a coordinator until 1985. In 1985 he was appointed professor of materials physics at the Royal Institute of Technology in Stockholm.