I am a Kenyan citizen and my US visas expired in December 2015. I was going back home to Kenya through London, and at Boston Logan airport I was refused to be allowed to board the plane as they said I can't transit through London with an expired US visa. I am going back home to Kenya to get them renewed, so what countries can I transit through now that London is out? I need to travel as soon as possible and really don't know what to do.
One option might be to transit through Dubai. From Visa policy of the United Arab Emirates:
Passengers on all international airlines may enter the United Arab Emirates for 96 hours after obtaining a transit visa at the airport. The time difference between the two flights must be over 8 hours and the passenger must continue to a third destination. Passengers also must have a hotel booking. 1
There are direct flights from Boston to Dubai, and from Dubai to Nairobi.
You can transit through the Schengen area without a visa provided you don't need to change airports. There are several possible itineraries which transit through various points in Schengen.
You can also transit through Doha, Qatar (ask BA if they can book this for you because it's on an alliance partner Qatar Airways); Dubai, UAE; Istanbul, Turkey; and almost anywhere else except the UK.