Late to the party, lol. The following is only true if you have a small hole in the round end (not hex end) of that fitting.
To me it looks like that is not a regular sort of fitting, it is an adjustable metering orifice for a gas valve on a stove. Don't know how proprietary it may or may not be. We've got a gas Tappan range from the late 40s or early 50s with a similar setup. The tighter onto the valve you get it, the less gas will flow. Ours has a needle on the valve side that is also removable. like this: valve--needle>--orifice hood. They came with different size holes for different flow rates (depending on if you were on natural gas, manufactured gas, or propane; and what BTU/h output the burner was.)
Hope you got what you needed. If not there's an appliance place here in town that probably can get what you need.