Why the Flower's 4-inch gun was not dual-purpose

Was the Flower-class corvette's 4-inch gun dual-purpose?

No. Its mounting did not have enough elevation to engage aircraft effectively.

This short answer clarifies the difference between carrying a useful surface gun and possessing a true dual-purpose battery. The Flower class's 4-inch weapon did not elevate high enough to engage aircraft effectively. Its limitation reflects the corvette's emergency escort role and the compromises accepted to put large numbers of workable ships into service. The watch point is useful when comparing nominal gun caliber with the mounting geometry that determines what targets a weapon can actually fight.