My gas furnace is hard wired to the main panel. In the event of an
extended power outage in winter, I'd like to have the option to run it
off my small Honda generator. The only real electrical draw is the
small 110V blower motor.

If we were in for an extended outage right now, I would probably just
jury-rig it with wire nuts and a sacrificed 12ga extension cord. I'd
like something a little more... sophisticated, something that is ready
on a moment's notice.

What if I:
1. Cut the existing hard line above the furnace and install a box with
an L5-20 twistlock socket.
2. Continue the hard line to the furnace from a second box adjacent to
the first.
3. Bug a short piece of 12-3 flexible cord to the hard line in the
second box.
4. Terminate the flexible cord with an L5-20 twistlock plug.

Is this kosher with NEC? Would running flex cable from the socket
clear to the furnace be a more acceptable solution?