EFF has previously examined silk and concluded, "We are generally satisfied with the privacy design of Silk, and happy that the end user has control over whether to use cloud acceleration..."
Also, it's possible the concept of 'trending now' may not impact user privacy - the whole point of Silk is that pages are partly pre-rendered on Amazon's servers, so it could be implemented as simply as seeing which parts of the cache are being hit frequently.
I don't really know much about how Silk is actually implemented, but it seems like all we know so far is that they're doing at least as much tracking as your ISP already is (and frankly, I find that much more concerning).
From a privacy perspective Chrome and Silk sound the same.
Now, maybe Amazon is more actively using that data and doesn't provide means to change privacy settings (Chrome allows you to locally encrypt). I dunno.
The real key to look at here is whether or not they are associating your visited URLs with your amazon account (or whatever account you need to be logged into. not a Kindle owner).
They mention they don't collect PII which doesn't mean it isn't being associated to PII though.
As long as the data is anonymized and aggregated properly and links with less then thousands of hits are never shown then there shouldn't be any problem.
One other interesting thing they could do with the data is if they started Amazon Search (they're caching a lot of the web as is) they could use their tracking of Google results to goose Amazon Search the way Bing did with IE tracking data.
Back when Silk first came out, they told the EFF that they don't send HTTPS traffic through their server. https://www.eff.org/2011/october/amazon-fire%E2%80%99s-new-b... But HTTPS obscures everything but the destination server. Even the rest of the URL should be invisible, so if Amazon is still tracking URLs, they are at least partly circumventing SSL protections.
https://www.eff.org/2011/october/amazon-fire%E2%80%99s-new-b...
I don't think showing sites that are trending in aggregate changes anything. This seems like a nonstory.