> The Amazon logo and the Amazon Smile mark are not permitted in third-party advertising by vendors and sellers linking in to Amazon. The “available at Amazon” logo is permitted for use in advertising.
Here's the "available at Amazon" logo: https://m.media-amazon.com/images/G/01/AdProductsWebsite/ima...
The main smile logo variants are also permitted for use in "logo line ups", "in a line up with two or more other retailers and not linking in to Amazon."
Most other uses are either not permitted, or subject to conditions, which sometimes involve obtaining written permission from Amazon.
That's just an example, other Amazon logos for other product areas - e.g. their app store - have similar conditions.
There may be some fair use exceptions to all this if used in a context that doesn't involve selling products.