Flak vs. lrm

Flak will win in theory.  The reason flaks beat LRM isn't because of a nifty damage bonus (their damage is actually quite low) but rather because they have a favourable armour type that reduces LRM damage and also an insane amount of health and shield at a very low cost.  The bottom line is that this will be a long and drawn out battle in which the flaks will win just because they have way more health than LRM's.

In practice, neither mass LRM nor mass flak will beat a balanced army of both LRM and flak.  Both of your instincts are wrong.  If you have mostly flak and few other unit types, a smart enemy will build some light frigates to counter your army.  He will use his LRM's to kill your other supporting unit types (including capital ships), and then his light frigates are free to kill your flaks at his leisure.  Mass flaks will not work in practice.

Similarly, if you send in mass LRM you've just opened yourself up to fighter or scout counters.  Without any compensating unit types he'll clean up your army pretty quickly, though you could potentially deal some damage this way before your LRM's go down.  I still wouldn't pursue this path, since you'd get a lot better performance out of a balanced army.

So you'd counter balance with balance?  Then just win with better skill or something?  I'd rather win with unit composition, LOL.

I guess the ideal counter to mixed flak/lrm is hc, but for this hypothetical let's assume this is unavailable, impractical to attain, whatever.  So hc is out.  What would you counter with?  In theory you could say "I'll counter his lrm with scouts or fighters, and I'll counter his flak with lf," but then his lrm will murder your lf, and his flak will murder your scouts/fighters.  That's why I said "all flak or all lrm."

So what fleet would you use against this fleet?

Try Carriers with Bombers a try? They're actually fairly effective against LRFs, and Flak doesn't completely annihilate them like Fighters. I'd try a combination of Carrier/Flak/LF against this match-up.

Early on, scout/LF will actually work.  Scouts can kill the enemy LRF fairly quickly, which then leaves only flaks that your light frigates can clean up.  With the right capital ship on the field, you can get a lot of momentum early on. This is particularly useful for Advent, but won't work as well for Vasari due to their weak LF and scout.  Support cruisers, particularly the hoshiko are great choices to back up your army since LRF and flaks generally don't kill them easily.

Carriers are a great selection.  Even if flaks are on the field, with the right kiting and maneuvering you can whittle down enemy LRF numbers.  However, this is definitely a more micromanagement-based army so if you want to win with pure army composition this isn't the path to follow.

The best counter to LRF/flak (repulse notwithstanding) are heavies, preferably backed up by support cruisers.  Unfortunately, it's entirely possible for Advent illuminators to brute force their way through enforcers with sufficient numbers, so Vasari is kinda in trouble, but in every other matchup heavies will do the job.  As you mentioned, they're also high in the tech tree and probably not viable.

Unfortunately, beating LRF/flak by army composition alone is very difficult.  It simply offers the best performance for your money, and between those two units almost every unit type in the game is countered.  You can counter it early-game quite nicely with scout/LF but that doesn't scale very well later on and a smart enemy will bring out his own counters anyways.  You can try carrier-spamming with bombers, but again a smart enemy will bring out his own counters.

Perhaps a worry about a Tec scout/LF fleet backed with hoshikos would be the very low dps?  Scouts only have the edge on LRF when massed, and the fleet just seems very vulnerable to the enemy capital.  An Advent colony ship could just ignore it, and kill scouts to level? And what is the right cap... any cap that the Tec use instead of a Marza, isn't helping to level a Marza.. a carrier is hindered by flaks and the Kol hardly ups the dps.  A Halcyon could kill all the scouts, and then you're left with LF..?  What Tec cap will push away a Halcyon?

The Illuminator bug doesn't help, but even when it is fixed it doesn't imply that Illuminators will be balanced- as the balance patch was meant to test whether the minor fix to Kodiaks and the LF buff had helped, I have to doubt it.  The bug was discovered in a balance Illuminators request thread...?  I'm very disappointed that there's no hotfix with the new beta, and if the concept is that we drift along with the bugged ships until they're fixed, and then more months with Illuminators that will still require an actual nerf, rather than these tweaks to other units, then I'm tired of it.

Please fix the Illuminators. 

Scout vs LRF isn't low DPS, and once the LRF are dealt with the enemy is also low DPS.  If the enemy can kill your scouts before you can kill their LRF, then you have problems.

Yes, that is the second weakness; capital ships fare much better against scout/LF then they do against LRF/flak.  However, it's all about picking the right caps and abilities.

If there are other units on the field, the smart player will ignore the cap and attack its support.  If it's just the capital ship, then even these units will take it down and force it to retreat.  The real danger here is of course the carriers caps, but it should also be noted that they threaten LRF-based strategies just as harshly early on.

Remember that flaks won't keep carrier caps under control, because carrier caps require no antimatter to replace their strike craft.

Try an Akkan with ion bolt.  Carrier caps are the most fragile of all capital ships, usually relying on kiting to stay alive.  I've killed more than a few carrier-first capital players by using Akkan or Jerrasul (gravity bomb) to cut off their escape while my "weaker" units kill them off.

well if u want spam vs spam JUST OUTNUMBER ur enemy's fleet like 2 to 1

well assuming that's an option, of course i would do that every time (and if 10 to 1 is an option, i would do that).  but this question is based on the assumption that both players have roughly equal resources and positions and fleet supply.  this is a question purely of "what is the best combo of units to build to counter X?"

I think flak do really well against ilums cause you can place right in the enemy fleet and soak up side beams while doing fair damage to lrf.It depends on situation and who your up against.I find that if its mixed flak and lrf you need something similar.I play advent alot and about 20 defense vessels along with 30+ ilums does well.As tec you could go hoshis with ALOT of flak.

The problem with going pure hoshiko/flak is that this just invites Advent disciple spam, which (now that LF have been buffed) is pretty dangerous. 

Yes well soon as he switches to lf start building lrf its a circle based on how good each player is to determine who will win.There lies the fun of the game