With the default gfortran checker options, it seems checking stops after the first error. You could try options that issue warnings that would otherwise be errors:
(setq flycheck-gfortran-language-standard "gnu")
(add-to-list 'flycheck-gfortran-warnings "pedantic")
Make sure fortran-gfortran is in your exec-path. (You can check your exec-path with C-h v exec-path.)
Or, explicitly set somewhere in your init flycheck-fortran-gfortran-executable to point to the executable.
Your warning messages (notice that they say "warning" rather than "error") come from flymake which is a package similar to flycheck except it comes bundled with Emacs. So those messages are not directly related to your flycheck config.