I admit I haven't played much multiplayer, but I have noticed that fighters are a good counter to bombers.  If I remember right LF are good against Flack Frigates so they might be a worthwhile counter.  As of yet I don't deploy flacks myself, but they do seem more effective in diplomacy.

My favorite strategy is to build bombers initially until the other races start deploying fighters in numbers.  Then I switch to fighters and rely on ship to ship combat.

Hope this helps.

Light Frigates. They're cheap and rip through flak and carriers easy. If you see your opponent going carriers and flak, answer with carriers, flak and light frigates. Your light frigates can tear down carriers health rapidly, and he'll be losing very expensive units to ones that aren't as such. Fighters will help thin out the bombers numbers initially, even if they all die to flak, that helps keep your light frigates alive to do their job. Bombers dont do crazy amounts of damage to light frigates, but they can still kill a bunch if your not careful. Just keep pumping them out and killing as many flak and carriers as you can until he starts pumping out LRFs to kill them off. If you can take down a significant number of flaks and carriers, you should be ok. It also might be a good idea to get in a pre-emptive strike. Flak and Carriers is a very cost heavy way to go, but can pay off big if significant numbers can be reached. If you can land a hard blow early, he'll abandon the idea and go lrf, which are easier to manage in large numbers. 

massed lf early on still not quite effective; destroying a carrier DOES NOT destroying its bomber instantly