As long as Amazon didn't know you were a California resident, you'd probably get away with it. However you'd be opening Amazon up to the possibility of a lawsuit from California. If they figure that out, they will not be happy with you.
Edit: definitely not a lawyer
Amazon is a significant source of income for me in California, and I was thinking of creating a California LLC this year anyway to shield from lawsuits. I'm now going to seriously think about doing it in Delaware instead.
Any advice?
Incorporating in Delaware does not necessarily make a corporation a Delaware resident only. If a corporation operates in California, it is probably subject to California taxes. In general, a corporation can be a resident of both the state of incorporation and the state of its principal place of business.
For sales/use tax, owning property in California or having regular employees in California may be enough.