If you want private prompting, run the AI locally. Everything else is just thoughts and prayers.

Given the issue with their browser and it's sneaky relationship with Microsoft I don't have a lot of faith:

https://www.tomsguide.com/news/duckduckgo-privacy-browser-facing-backlash-over-microsoft-trackers

In saying that the name is cool because it will possibly attract users who type "fuck AI" and it autocorrects to "Duck AI"

Personally I try not to interact with AI prompting because of the Uncanny Valley feeling but I have found Braves Leo AI to be good - but my lack of AI experience doesn't qualify me to rank them.

When looking at privacy concerns with Leo AI all that comes up is the communities voice and no actual privacy issues (to date).

https://brave.com/leo/