Yes , it matters, it must be a standard shaft
heres a suggestion.... drill the extension out to accommodate the size of a quick connect bit, and use the set screws to hold bit in place.
This Flex Bit Extension is intended for use with Klein Tools Flex Bit Augers 9/16'' (14 mm) and smaller (Klein model # 53716, 53717, and 53718). These Flex Bit Augers are made to drill through wood, not steel. Klein Tools does not recommend using more than 1 extension (approximately 9 ft. total length when attached to a Flex Bit Auger). If additional extensions are added there will not be enough torque to drill a hole.