Most all wine kits are 6 gallons. All the beer buckets I have are 6.5 gal to the top which will probably work for your kit but you'll have to watch it closely. Measure your bucket with a measuring pitcher or gallon jug. If it's 6.5, try it, and if it foams up, be prepared to transfer some of the must to a 1/2 gal. growler or 1 gal. glass jug with an airlock.
It's very useful to have larger fermenter buckets, especially if you get into fermenting high end kits with grape packs, fresh wine grapes or other fruits. Most LHBS have food grade plastic barrels in 10, 12, 20, and 32 gallon sizes, and it works just fine to ferment 6 or 6.5 gallon batches in a 10 or 12 gal barrel. You can also use them for beer, and even do double batches. It eliminates much of the problem of foaming over.
I have several 6.5 gal. brew buckets, a couple 12 gal., six 10 gal. Brute barrels (which are my favorite), and two 55 gal. barrels for fermenting. During fall harvest, we often have all in use at once.
Here are some apple cider based wines in 10 gal. Brute barrels, cranberry apple in back. dry apple, spiced apple and some cran-apple syrah.
Having various sizes of primary fermenters and carboys will give you a lot of flexibility.