The odyssey and the conquest can both fire broadsides without going above 5% so long as they’re not taking incoming fire.
Considering that this gives them destroyer speed or better (forward speed is faster and more maneuverable than backwards/side to side speed) it lets them safely and powerfully engage around the periphery and clean the enemy force up.
But it's not about average flux usage - it's about not having 5% even for split second. Since weapons consume flux in bursts, most of them fail to maintain strict below 5%.
...Though I guess, it's possible to pick some weapons which do work for Conquest, like Storm Needlers. Or raise caps just to go below magic 5% peak, if you are otherwise close to it. Not sure if it's worth doing though, since it means sacrificing stuff like Gauss Cannons (too much flux per shot no matter what you do).
Conquest can fire 2 gauss consistently without going over 5%. It costs 2400 flux and 1200 of that is burned away as you fire. Putting you at 6% of cap assuming no skills or increased flux capacity/vents... which well... you should have
Edit: like, if you fire sequentially it’s possible to keep under 5% cap with zero skills or extra vents. It’s totally easy with them.
Though to be fair my ideal conquest is
Side 1: Gauss and whatever single flack or dual flack work but are not necessary
Missiles: 2x MIRV + 2 x Harpoon Pod
Side 2: devastator cannons and flack.
Mjolnir works as a decent sub if you can’t get gauss.
Edit2: the gauss in sequence flux lock and then The MIRVs and harpoons kill them. If you’re re against a fighter heavy force or about to suffer a bombing run you pop the maneuvering jets and swap sides.