I have finally go my hands on the same thermocouple that I believe you are using
The label on the box says:
114653 Kit,
Thermocouple
Street W/Harness
Stewart Warner Performance
I hooked the red wire to FlashScan's Alumel (-ve) terminal (Pin A).
I hooked the yellow wire to FlashScan's Chromel (+ve) terminal (Pin B).
See image attached for pinouts.
I tried it connected directly the the short (8 inch) red and yellow wires - that worked ok.
I tried it with the red/yellow (in brown cover) extension wires and that also worked ok.
I measured iced water at 9 Deg C and a naked flame at 405 Deg C.
Did you ever get a different k-type thermocouple to work with FlashScan?
If a different k-type does not work with FlashScan then it may be a faulty FlashScan unit.
If a different k-type does work with FlashScan, then it may be a faulty Stewart-Warner thermocouple.