Flame Arrows says that:
The spell's magic ends on the piece of ammunition when it hits or misses, and the spell ends when twelve pieces of ammunition have been drawn from the quiver.
Does the Flame Arrows' magic end on the pieces of ammunition when the spell ends, even though the spell does not say so?
If so, then Flame Arrows effectively only enchants 11 pieces of ammunition because the magic ends on the 12th piece before you can fire it.
On the other hand, if Flame Arrows' magic does not end on the piece of ammunition when the spell ends, then nothing is stopping me from stockpiling several dozen enchanted arrows days in advance.
The first reading seem weird and disappointing, while the second one is even weirder, but I do not see an alternative. If either reading were the intent, I would expect the Flame Arrows to be more explicit…
Best Answer
The spell's magic ends when the spell ends
Since the spell has a duration that is not Instantaneous, it will cease to persist when the spell ends, causing the effects to end.
What happens to the 12th arrow?
While intuitively, you draw the arrow before firing it, in the rules these events are concurrent. This means the twelfth arrow is fired at the "same time" as it is drawn (assuming you draw it as part of an attack and not just to pull it from the quiver) and will still be affected by the spell when it hits (or misses).
Here is the rule on Ammunition weapons from the Player's Handbook:
It is also worth noting that the arrows are not enchanted
The quiver is actually the only thing affected by the spell (and eventually any target hit by a ranged weapon attack).
This quote from the spell shows that the ammunition is still mundane but the fact that it was drawn from the quiver grants the effect on hit.