Get some fast mechs, as heavy as possible, to get into Flagg´s back and kick him. His Cyclops is too poorly armored to take very much of that. Preferably use jump-capable models - Griffin, Wolverine, Shadow Hawk, Dervish, Phoenix Hawk, the JJ-equipped Trebuchet variant, you know what I mean.
Generally, I´d concentrate on the bodyguards first, taking them out one by one - although, for "taking out", knocking out the gyro or or giving them a hip crit should be more than enough. Then, use Flagg´s impulsive nature to lure him out of the field of fire (or out of range) of his now near-stationary bodyguards. Once he is there, kick him, preferably from behind, until the Cyclops goes down. Not shooting at him presumably means that there is little torso damage, and very little chance that fall damage sets off any ammo.
All the falls and failed attempts to get up should give Flagg pilot hits, meaning he´ll black out sooner or later. One Mech now starts extracting Flagg, the others - in case he isn´t knocked out long enough - use aimed fire to (carefully, to avoid torso damage) shoot off his legs and arms. With no arms and legs he can´t stand and can´t prop up to fire, so even if he regains consciousness, he´s incapable of defending himself.
My TOE:
2x GRF-1N
2x DV-6M
2x PXH-1
2x PXH-1D
2x JVN-10N
2x FS9-A