The flashlight should maintain a current draw of 3A that's why it says regulated.
You measured 1.2A -1.28A, that means 2.4A - 2.56A, That is the current drawn by the driver. According to the specs it should have been 3A. 1.5A since there are two batteries in series. However that is the input current, not the output current.
You should also try to measure at 3.7v to see if it will draw the same current until that voltage.