They address this on their website and go in further detail on their privacy policy. You'd have to read through that to decide if they do enough to earn your trust. But in my opinion not having any advertising removes most of their incentive to try to collect user data. I suppose there could be a temptation to collect the data to resell, but since a large portion of their income relies on the reputation of being a search alternative that has a focus on privacy I feel the risk to their reputation would be greater than whatever revenue that would generate.
Of course there are all kinds of companies that flew too close to the sun and sold out user privacy for a Coke and a smile. I've decided to go with Kagi and have been very happy with them so far. If they ever sell out I'll cash out, but they seem to be the best option for me right now.
Kagi has been great. I'd like to see more searches on their $5 plan as 300 searches a month doesn't feel adequate. It has been great being able to promote, demote, and block sites from searching and I have found my results to be more helpful and relevant than Google alternatives I tried. I don't think I have used Google search at all since signing up. Highly recommend.