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Amazon is considering shoving ads into Alexa+ conversations
(arstechnica.com)
This is a most excellent place for technology news and articles.
Depends on the model and firmware, but for most, Winterbreak is the current method.
Do note if your Kindle is updated to version 5.18.x currently it's not possible to jailbreak. There is ongoing work on a new exploit though, and a new jailbreak method (or update to Winterbreak) is expected later this year.
Edit - actually, if you're on firmware 5.18.0 the jailbreak may work. 5.18.1 and above it definitely doesn't.