This seems technically possible if you support multiple backends simultaneously.
Sadly, PortAudio does not support opening a full-duplex stream where the input and output devices are on different backends (Host APIs). Adding such support in PortAudio, or implementing it directly in FlexASIO, is not trivial. I wouldn't expect this feature to be implemented any time soon (or ever).
There's another potential problem with regard to using ASIO as a FlexASIO backend. ASIO was never designed for multiple drivers to be used in the same process - it uses global process state which gets in the way. I suspect that's a problem that can be worked around with some trickery, but it makes things more difficult.