So if I've got this right, you've basically got a fairly stock TPS deck with:
2 Needlebite Trap
2 Punishing Fire
4 Grove of the Burnwillows
Is that right?
With Delver, Pyro, and Mentor pushing the creature wars back into Vintage, Punishing Fire/Grove of the Burnwillows seems strong.
First, I agree but I think you're in completely the wrong archetype.
For the most part, these grow decks don't kill very fast. Even with a strong opener, you're likely to have several turns pass before they're threatening lethal. You should be killing these decks before it matters. Instead of strengthening your matchup against these decks by answering them, strengthen them by just winning.
Looking at some of the recent 4-0/3-1 storm decks on MTGO, only a few played anti-token cards and all of them were sweepers. A couple decks played Massacre (so I suppose they're not worried about Young Peazy at all) and one played Thrashing Freaking Wompus and needs a high five from me.
Oh, also, I don't like the idea of playing 4x a card that gives your opponent life in a deck trying to win with Tendrils. Your job is a lot harder if you draw Punishing Fire when you wanted a real dual.
Second, while Punishing Fire might be a neat thing to try in Vintage, I don't think "answering tokens" is the role it needs to be filling.
1R to kill 1 Young Peazy OR 1 Elemental token OR
maybe kill1 Monastery Mentor OR
maybe kill 1 Monk token is some pretty awful value. For 1R you could have Electrickery doing 3 of those 4 things to the entire board. You could also have Pyroclasm doing 4 of those 4 things to the board.
I think if Punishing Fire has a place in Vintage, it's in something like it's place in Legacy - killing value creatures and grinding away at opponent's life totals in a long, grindy game.
Needlebite, while underrated, is strong and hilarious against storm.
It might be hilarious but I don't think that it's actually good.
The only time that they're gaining life is when their Tendrils of Agony has been placed on the stack, Storm has triggered, and the copies have begun resolving. The end result is that they drain you (but maybe not enough to kill) and they gain a bunch of life, making your job of Tendrils-ing them to death that much harder. I think I'd rather have counter magic like Flusterstorm or Mindbreak Trap in just about 100% of circumstances. Plus, it can be used mid-combo, making their ability to strip your hand slightly less relevant.
I think you probably put it in there for its ability to kill. That requires two major circumstances. First, your opponent must be at 3 or fewer life when Tendrils begins resolving (because they'll gain 2 before you can "Trap" them). Second, your opponent must not have made you discard this card.
For situations where you're not killing them, all you're doing is saving yourself. And even saving yourself requires that the storm count be less than x+3 where x is the amount of storm required to kill you without having trapped them.
So let's say you don't kill them but you do save yourself. What now? You're at a severely diminished life total, so something as simple as Yawg's Will > Tendrils might be enough to kill you. They've gained a bunch of life off their Tendrils, making your job as a storm pilot all the harder.
I suppose the one redeeming factor of this card against storm is that you might actually just cast it as a 7 mana (or free off Mind's Desire) drain 5.
