Catalyzes the ATP-dependent phosphorylation of fructoselysine to fructoselysine 6-phosphate (PubMed:12147680). Functions in a fructoselysine degradation pathway that allows E.coli to grow on fructoselysine or psicoselysine (PubMed:12147680, PubMed:14641112). To a much lesser extenst, is also able to phosphorylate psicoselysine (PubMed:14641112). ATP + N(6)-(D-fructosyl)-L-lysine = ADP + H(+) + N(6)-(6-phospho-D-fructosyl)-L-lysine Carbohydrate metabolism; fructoselysine degradation; D-glucose 6-phosphate and lysine from fructoselysine: step 1/2. Monomer. Induced by fructoselysine and psicoselysine. Makes part of the frl operon with FrlA, FrlB, FrlC and FrlR. Belongs to the carbohydrate kinase PfkB family.