Catalyzes the phosphorylation of D-allose to D-allose 6-phosphate. Has also low level glucokinase activity in vitro. ATP + D-allose = ADP + D-allose 6-phosphate + H(+) Catalytic efficiency with D-allose as substrate is 735-fold higher than that with D-glucose. Carbohydrate degradation; D-allose degradation. Belongs to the ROK (NagC/XylR) family.