Evasive action the moment it starts to take excessive kinetic damage when near flux overload sounds good
Kinetic weapons are often the fastest and most accurate weapons. Dodging them in their current form is not really an option. And you have to see just how fast MGs and needlers take flux off from shield. With a ship focused on kinetics or swarm of broadswords, it takes like 3 seconds or less to go from zero to overload.
Given that flux overload is the most devastating status to be in outside of death, this makes kinetics weapons easily the most versatile weapon, and they are rightly highly priced. Yet these automatic kinetics still easily make up for their ordinance cost by 'flux-overload-locking' AI ships' down.
What SQW said is probably the easiest fix... as Alex said, the decision making of whether to take hits on armor or use shield to absorb as much as possible may seem intuitive for a person, but coding it into functional AI is another matter. Another method is to simply stop AI from ever using shield when in danger of flux overload, which would help it against kinetic spam, but not sure how that would work against other weapon types.