What is the highest degree held by Freeman Dyson?
According to both Freeman Dyson's homepage at the IAS and the accompanying C.V., he never earned another degree after his B.A. While unusual, this was much more possible at the time, since research in general was less well supported and organized.  A number of other notable contemporaneous researchers (e.g., Ed Fredkin) also never earned a doctorate.

In the modern world, this is much more difficult, though similar recognition can be obtained as, e.g., a Professor of Practice.