[tomsem]

When I did first Web search on my Fire Max 11 (just now) it prompts for browser choice (in my case Firefox or Silk) and offers Just once or Always choice. I chose Always, and the next Web search launches Firefox, as expected.

I don't know how you get it to ask again after selecting a preference. But it seems yours is set to 'Always use Silk'.

Surely there's some way to do it short of Reset to factory settings? Maybe go back into Default apps, select Silk, then set it back to Chrome?

There's also a Reset app button.

Finally if you go into Kindle APP settings there's an Allow App to open supported links. You can choose Ask every time. Maybe that will let you re-select default.