A flat flame oxy-fuel burner including a gaseous fuel nozzle having a hydraulic diameter Dh-NG and a width to height ratio w/a of at least 2; a primary oxidant conduit surrounding the fuel nozzle to form an annular primary oxidant nozzle between the fuel nozzle and the oxidant conduit, the oxidant conduit having a height b, the respective outlet ends of the fuel nozzle and the oxidant nozzle being aligned; and a precombustor extending from the outlet end of the fuel and oxidant nozzles and having a length L and a hydraulic diameter Dh; wherein the ratio L/Dh is non-zero and less than or equal to 4; wherein the ratio L/Dh-NG, is non-zero and less than or equal to 12; and wherein the dimensions a, b, and w are sized to yield a primary oxidant Reynolds number from 200 to 22,000 during burner is operation at 0.05 to 1 MMBtu/hr.