At that age, I would think letting them do it on their own via a direct LHR-BOS flight would be fine. Navigating passport control and customs at BOS is incredibly easy in my opinion, and the staff are generally quite friendly and accessible given the relatively small size of Terminal E.

I myself considered something similar a few years ago for my niece, but given that she was much younger at the time, the lack of a UM service on BA meant I ended up choosing to do back-to-back LHR-BOS-LHR flights to pick her up and then drop her off.

I would second the suggestion made above of ensuring they have with them a U.K. phone with international roaming enabled (most of the U.K. carriers have in recent years started offering some inexpensive plans that include free roaming in the US - I know from personal experience that Three and Vodafone certainly do). They can then also freely use their U.K. data/voice allowance to stay in touch with family members in the U.K. throughout their stay in the US (if that is desirable).

Might also help for them to carry a letter from the parents, stating they have permission to travel and containing the contact details of both the parents and the family members they will be staying with in the US. Might not be needed, but handy to have in case border control start asking questions.