This most likely points to a fault in the built-in flash circuit rather than the whole camera. On cameras like this, a flashing battery icon can act as a general error warning, and the clicking you hear strongly suggests the flash charging circuit is failing to reach full charge—possibly a bad flash capacitor or related component.

Since you already tried fresh batteries with no change, weak batteries are unlikely to be the cause. It’s best to stop trying to use the flash, because repeated failed charging can worsen the damage.

If the rest of the camera works, you may still be able to use it without flash. But repair is usually not economical on an older EOS film body unless the camera has sentimental value or you have access to a specialist repair tech. In most cases, replacing the body is more practical than repairing the built-in flash.