I'm not familiar with OmniForm, but doubt that there are any built in ways to move data from FileMaker to OmniForm or vice versa. You may find that OminForm can import data from a typical data exchange file format such as tab delimitted, csv, xml, or Excel. Since FileMaker can export into such formats, you may be able to export from FileMaker and import into OmniForm.
I don't think you can display the OminForm file in the container field so that you can see its contents. You can with a PDF of the form on Macs and you can display PDF contents in a web viewer on both platforms.
Also, if you insert the OmniForm file into a container field with the "store by reference" option, you can double click the container field to open the file in OmniForm for editing.
Given those limitations, why do you need to use OmniForm in the first place? Perhaps there's a way to use FileMaker that eliminates the need for this application.
But our company uses Omni Form for its needs, and It appears I will need to just continue using it as
a second double entry program. Thanks for the input and the suggestions.