Flak Frigates have heavy armour, and the only unit in the game that has an advantage against heavy is the light frigate. Unfortunately, Vasari has the worst light frigate of any faction, the Skirmisher. It's very expensive, but pound-for-pound both the Disciple and Cobalt hit much harder. As well, you're very vulnerable to enemy LRF with this unit (though not so much the Advent Illuminator). Aside from that, enforcers will work. They don't receive any penalties when attacking light armor, and their very heavy armor makes them close to impervious to the flak frigate's damage.
The bottom line, though, is that the Vasari faction's best units are all the phase missile units, and flaks force you to counter with units that don't use phase missiles, so this strategy inherently forces you to build your worst unit types, making you easier to counter overall. You can fill out your force with your Sentinels, which do use phase missiles and will help counter enemy LRF as well as fighters and bombers.