It's okay to be wrong

When creating on-the-fly rulings for nonstandard maneuvers, you and your players should understand that snap decisions may be revisited once given more time. Keep the communication open with your players and come up with something that works for everyone and that makes logical sense for you and them.

On the Fly - Rule of Cool

As I said above, it's absolutely fine to make a quick call and realize you made a mistake later. The guideline at the table should be "Have Fun" - so the Rule of Cool comes into play. Don't let it break your encounter, but if it does because the idea was that good - roll with it!

Specifics - The Flaming Arrow

There are some things to consider with this example. How are they lighting the arrow? If they're pouring oil, lighting it, and firing it - that is some action economy to consider. The pour/light might be an action, with another to fire it. Allowing you to roll that into one single action doesn't make sense with action economy. In addition, an arrow on fire it pretty just going to douse itself once it sticks into someone. I don't really see how damage gets transferred in a way that Poison would.