Listen, if your kid trusts you enough to ask for a burner, help them. Wipe your old phone or find something cheap, teach them about threat models, private browsing and factory reset, then teach them how to teach these things to other people. The only question you need to ask is, is this for you or for someone else, and you don’t ask who or why.
You don’t need to make the first conversation perfect, you need to make the next conversation possible.
My son recently set up his FOSS phone. I can't give much better detail than that, but those who know will know, and for those who don't - it is not an apple or an android or a windows phone. Nokia doesn't have an OS, right? If they do, it isn't that either.
He has zero log-ins for apps & accounts of any kind (except his mastodon account). He's actually pretty fantastic & groovy, my kid, but also, he's been willing to help others achieve the same!
He is willing to help people away from corporate overlord cell phone control. I was not commenting that he is helping people with domestic abuse problems. However, I do believe FOSS software could help in some of those situations. Having apps that are not tracking you or having the better ability to control your software could definitely help!
I appreciate you sharing your concern. That is a point to make. Frankly, any departure from corporate overlords is a boon to us all.