You’ll have to reach a desired speed using autothrottle speed mode and then set FLC. I’ve not seen a solution where FLC hold properly if you simply turn it on without use of autothrtottle. IIRC, I’ve also noted if you subsequently turn off FLC and then turn it back on or attempt to adjust autothrottle speed settings during the climb, it doesn’t necessarily do what you’d expect. I don’t believe it’s modeled very well. When I have been performing testing on my modifications, I first set desired altitude. Then I set autothrottle to desired speed hold and once I’ve reached that desired speed, turn on the autopilot and FLC mode. Oh, and then once I reach around 30k feet where the speed mode needs to be switched over to Mach hold, the FLC will not adjust the Mach number with altitude, so it will continuously drop the nose as the effective Mach speed gets unreasonably high effectively ending the climb early. I believe this is a known bug. I have to switch over to VS hold and then babysit the VS until reaching cruise. So, in summary, FLC is hard to use and doesn’t work particularly well in the upper flight levels.
If anyone else has better procedures for getting FLC to work properly please let us know.