Catalyzes the ATP-dependent phosphorylation of D-threonate to D-threonate 4-phosphate (PubMed:27402745). Can also phosphorylate 4-hydroxy-L-threonine, with lower efficiency. This side reaction may serve to deal with the toxicity of 4-hydroxy-L-threonine by converting it into 4-hydroxy-L-threonine 4-phosphate, a useful product that can be used by PdxA2 (PubMed:27402745, PubMed:27294475). ATP + D-threonate = 4-O-phospho-D-threonate + ADP + H(+) kcat is 22 sec(-1) with D-threonate as substrate. kcat is 4.0 sec(-1) with 4-hydroxy-L-threonine as substrate. Deletion mutant is unable to use D-threonate as a carbon source. Belongs to the four-carbon acid sugar kinase family.