According to this ticket on the stack issue tracker, Stack can currently only build documentation for libraries, but not executables.
Cabal can be configured to work with the stack databases with this command:
cabal configure --package-db=clear --package-db=global --package-db=$(stack path --snapshot-pkg-db) --package-db=$(stack path --local-pkg-db)
after which you can run cabal haddock --executables to generate the documentation.
By the way, stack haddock is only a shortcut for stack build --haddock, so there is no need to write stack haddock --haddock.