The wood chews are absolutely fine, though you could probably find them in bulk online for much cheaper.
As for the food and such, Kaytee feed is not the greatest feed. It contains preservatives that are not good for chinchillas. I would bring it back and go with a higher quality feed like Mazuri, PANR, Tradition or Oxbow. I sell PANR and Mazuri, and I know others on here sell Tradition and Oxbow. Even with shipping the prices for PANR are cheaper than anything you would buy in a pet store.
As for their hay it's hit or miss. Sometimes it's fine, other times it's old and brown. If you use Kaytee hay just make sure go for the freshest looking mini bag you can find. Oxbow is a bit more expensive ($10.00 for 40 oz.) at PetSmart but is really worth the money. My chins eat more Oxbow hay than they ever did the Kaytee hay, so even though it costs a little more, the chins are actually eating more and you are throwing away less. When you open the Oxbow bag you will see (and smell!) the difference between the hay.
In terms of bedding, Kaytee is absolutely fine. Aspen is aspen is aspen, and it really doesn't matter who makes it. Pine bedding is also fine to use. I prefer Aspen as the pieces are usually smaller and easier to vacuum from the floor, but other than that both are fine to use.
For dust, I would recommend going with Blue Cloud or Blue Sparkle. There are a lot of sellers on here that carry it. The difference in a chin's coat dusted with either of these is amazing. When I first got my chin I used the Kaytee dust. I decided to try someone with Blue Sparkle and the change was AMAZING. I now use Blue Cloud, but either of them are great. Again, even with shipping you will probably be paying less for the higher quality dust than you would for a smaller container of Kaytee dust.