Ahem! Ex-FLM here.
It wasn't possible to go any further than SAC in my days as a FLM - it
was possible after a spell of time on the job to go on to what was essentially a Direct Entry fitter's course in your chosen (or available!) trade.
FLM was a basic but very hectic job depending upon what aircraft type or the function the squadron or unit performed. Happy days...
The extra pennies following the fitter's course were very welcome though!