Catalyzes the ATP-dependent phosphorylation of D-erythronate to D-erythronate 4-phosphate. Can also phosphorylate D-threonate and 4-hydroxy-L-threonine, with lower efficiency. ATP + D-erythronate = 4-phospho-D-erythronate + ADP + H(+) kcat is 16 sec(-1) with D-erythronate as substrate. kcat is 12 sec(-1) with D-threonate as substrate. kcat is 41 sec(-1) with 4-hydroxy-L-threonine as substrate. Belongs to the four-carbon acid sugar kinase family.