So we can actually figure out how much flux the Gigacannon uses per second by the screenshot in the blogpost.
We know that at the time of the blogpost, Kinetic Cannons are 400 flux/second[1]. The screenshot Executor has 5x Heavy Needlers, 4x Kinetic Blasters, 4x Burst PDLs, 1x Dual Flak and 2x Gigacannons; for a weapon flux/second of 3210.
So the flux/second of its weapons that we know about are 5x200 + 4x400 + 4x40 + 150 plus two Gigacannons. That means a Gigacannon uses ( 3210 - 2910 ) / 2 = 150 flux/second.
Which means the Gigacannon must be really, REALLY slow-firing as it uses barely more flux/second than the small AM blaster.
[1]
Spoiler
It has the same anti-shield DPS - and pretty much all other stats except for flux cost - as a Heavy Blaster; I'm still working out what the flux/shot should be. Right now it's at 400 (for 250 kinetic), which has felt ok in testing but sounds a bit too low on paper; maybe it ought to be 450... it pretty clearly ought to be below 500, though, so that it's better anti-shield than the PL.