Company-flex only works with the company-capf backend. Most sources use this backend, with the exception of the more advanced sources. Most backends should be re-written in terms of completion-at-point-functions eventually, although it's going to take a while.
I have not considered this option so far.
I glanced company-capf code, and I think it is possible.
I am not yet sure whether there is any downside or how much work is required for this.
Citing from the the tool's site [1]:
Is it possible that company-ghc use capf?
[1] https://github.com/PythonNut/company-flx