Amazon stores aren't too easy to navigate in, so you would expect them to allow you to search them, but I don't see that option on my create Amazon store or on widgets or in the store preview. Do they have it?
I don't think they have that option, other than an extensive navigation bar. I you're serious about creating an Amazon store I'd suggest the Associate-O-Matic script.
They are as easy or as hard to navigate as you set it out to be. Aside from sales, which I think is still zilch from my aStores, the whole idea is for you to set up small niche sites same as what most of our members have done it with ASM's or Assoc-o-Matic's. These niche stores then can be actually easier to navigate and I find that search could also be easier.