。
My eyes are being dazzled.
Literal
Eye [subject-が] dazzle-dazzle does.
チカチカ is a mimetic for flickering, twinkling, or glaring light — a loose lightbulb, a stroboscope, sun on snow. 目がチカチカする is the standard way to complain that your eyes are being overwhelmed by harsh or flickering light. Like other mimetics, it pairs with する to form a verb.