The army of the dead is heading south and though Jon is doing everything he can to prepare the living, it still may not be enough. However, with Daenerys and her dragons now in Westeros, they could provide another essential weapon against the White Walkers. So can dragonfire kill White Walkers on Game of Thrones? It definitely seems plausible, though it has yet to be proven.
Thus far, there are two known materials that can kill a White Walker: dragonglass and Valyrian steel. Dragonglass is actually just obsidian, or volcanic glass, and Sam has just confirmed that there's a whole mountain of it underneath Dragonstone, which is where Jon is now headed. Differently, Valyrian steel is forged by magic and dragonfire. Valyrian steel is now very rare, as dragons went extinct (until now) and the steel was forged in Valyria, which is now a ruined city.
Because Valyrian steel is made from dragonfire, it seems fair to assume that dragonfire can kill White Walkers, just as regular fire kills wights, the animated dead people that White Walkers create. However, this theory can't be proven until the dragons come face to face with the White Walkers, and it could be disastrous if this theory is proven wrong.
Whether or not dragonfire is the answer to Jon's prayers, he still needs Daenerys help for the upcoming war against the army of the dead. The cache of dragonglass could form plenty of weapons for the living to use against the White Walkers, so even if dragonfire doesn't work, it's already known that the dragonglass will.
Jon will most likely do whatever it takes to get that dragonglass from Daenerys, which really puts him at her mercy. However, Daenerys could use Jon on her side as well. The war for the Iron Throne has already begun and Cersei drew first blood, even though she doesn't even know about it yet. Euron attacked Yara and Theon's ships, and took and/or killed Yara and Ellaria, two of Daenerys' best allies.
An alliance with the King of the North could be beneficial to Daenerys, especially since many view her as an outsider in Westeros. Not to mention, Jon could vouch for her and stand against the claims that she's just as mad as her father was. Basically, this partnership could be a win-win for both Daenerys and Jon.
However, will they be able to come to agreement that works for both of them? Thankfully, fans won't have to wait long to find out.