As of the patch 1.72+ (January 22, 2020) the Flare Gun no longer appears to deal damage to animals (in Survival and Wintermute). A shot flare from the Distress Pistol will merely bounce off an animal during collision and fall to the ground where the animal was standing (resulting in no 'instant-kill' or 'bleed out' effect). AS normal though, the animal will always be scared afterwards and run away.
Whether this is a bug or intended feature is unclear, since this is not displayed in the Hinterland patch notes/changelog.