Catalyzes both the phosphorylation of dihydroxyacetone and of glyceraldehyde. ATP + dihydroxyacetone = ADP + dihydroxyacetone phosphate + H(+) ATP + D-glyceraldehyde = ADP + D-glyceraldehyde 3-phosphate + H(+) Belongs to the dihydroxyacetone kinase (DAK) family.