It is permissible to run four #6 THHN copper through a 3/4" flexible metal conduit (FMC). That will give you a 65 Amp circuit. If you use #8 it will be rated for 50 Amps.
It is very difficult to pull 90 ft of it through FMC, and I expect impossible to pull it through the INSERT connectors. You will need pulling lubricant.
It is not a "code" practice, but if faced with the problem I would pull through the FMC and then put the connectors on the ends and connect to the box after the wire is pulled. You will need to fasten the conduit in place while doing the pull.
If you have a balanced load such as a dryer or water heater circuit you should be able to run #8 copper for the neutral and #10 for the ground for up to a 60 Amp breaker. If the breaker on the feeder is more than 60 Amps then you need a #8 ground.
If you are not attached to using the old FMC you can run aluminum SE R which is a 4-wire cable that needs no conduit. #2 is rated at 90 Amps and #4 at 65 Amps. The aluminum is fine for a subpanel feeder.