If I activate Jendon with Flight Controllers, and use Jendon's ability to permit another squadron to attack, does that squadron benefit from Flight Controllers?

No, because the attacking squadron isn't being activated, which is the criteria for applying FC:

Gotcha.

Jendon allows you to attack with a squadron, even if it has already activated.

Can I then activate an unactivated squadron through Jendon to reap the benefit of FC, or are all Jendon taps unactivated?

If you are using Relay , and the ship performing the command has Flight Controllers, than anyone accepting the order through Relay, will be boosted with Flight Controllers. (And not just flight Controllers - anything that applies to Squadron Activations from the Ship - Such as Vector counts, too).

But if it is Jendon himself that is providing the opportunity to Shoot, through Jendon's special ability - then No.

Look that FC works until the end of the squadron activation so you cannot activate a squadrons giving the blue die and then activate Jendon and attack again with the already added blue die wih the same squadron command.