Advanced Benefit: You can impart a powerful spin to a thrown starknife so that multiple blades strike the target rather than just a single blade of the four, dealing extra damage with the other blades. As a full-round action, you can make a single attack with a thrown starknife, rolling 1d4 to determine how many effective strikes you gain with the attack (if you roll a 1, then only one blade strikes). If the attack hits, all of the effective strikes damage the target. Apply precision-based damage (such as sneak attack damage) and critical hit damage only once for this attack. The damage bonus from your appropriate ability score modifier applies to each strike, as do other damage bonuses, such as a bard’s inspire competence bonus. Damage reduction and resistances apply separately to each strike.
Ordinarily, I'd say yes, but I came across this thread about it while I was looking up other things, and it made me wonder if it would or not.
So I came here to see if SE can answer the question, does Desna's Shooting Star get the benefits of flaming (or other similar enchantments) on it's initial hit and each effective hit?