I would think 6 Corners gets even better with Next Destinies, for several reasons:
Prism Energy. This is such a useful tool; it's even better than upping the Rainbow count to 8 if that were legal. Other decks make use of this, but none so much as 6 Corners, which uses a lot of different types of energy, even in the same matchup.
Skyarrow Bridge. Again, a lot of decks will use it because Basics are so big right now, but Six Corners gets some 1-retreat or even 0-retreat Pokémon with this in play, which changes games.
EXs being worth 2 prizes. This might seem like it would benefit every deck, but 6 Corners gets a bigger boost because its main goal is to hit for weakness or at least win the prize battle. For every EX deck, you can bet 6 Corners will have a counter, and so the high HP on EXs isn't even so bad for it as it would be where you're trying to beat Mewtwo EX with, say, Reshiphlosion. Being able to hit for weakness, or at least get consistent 2HKOs on every EX, will help this deck more than most others.
There are some cons to ND for 6 Corners– for example, neither Heavy Ball nor Level Ball aid it as much as most of the meta– but far and away, I believe Next Destinies will only help the popularity and success of Six Corners.