Flaks receive less damage from (Tec and Vasari) LRMs due to armour type and do more damage to LRMs due to damage type they do.
Flaks also have the advantage that if you position them right they fire at multiple targets at the same time, which you cannot read out of the damage charts(!).
Additionally Flaks have much HP and armour, giving them some staying power vs LRMs.
Flaks are not the "perfect" counter, fighters and heavy cruisers are more effective at killing LRMs quickly.
However, flaks need only two labs and thus are easier to reach than carriers or even heavy cruisers if you are under LRM pressure.
Also, their high HP and armour lets them hold out a while vs smaller numbers of their direct counters too, if that should be necessary.
The multiple weapon arcs and sturdiness combined give the flak a significant long term advantage in fights vs LRM blobs, if both fleets consist of comparable resources (The flak fleet can have somewhat less resources as flak ships than the LRM fleet and still be victorious, but 5 flaks wont win vs 40 LRMs...

)
The same amount of resources in flaks will defeat the same amount of resources in LRMs easily and with few losses in "sterile" fights.
Of course, as posted already, a pure LRM fleet will seldom fight a pure flak fleet, and once you have a big flak fleet but the enemy stopped building LRMs (and carriers) that many flaks become somewhat useless...
In conclusion however flaks are a cost effective and easy to unlock way to bolster your fighting power vs LRM-mostly and LRM-only fleets.
Incidentally there is much whining about LRM spamming... so it might be helpful if some players try it for themselfs or simply accept that on a per resource basis flaks beat LRMs.
I think they like them because they see that raw damage is 19 or whatever while light frigs have 11 dps, not realizing there are different damage types.
Interestingly flaks will be like 5 times better at fighting LRMs than light frigates... since LRMs are the direct counter to light frigs.