[DerekM]

tell application "OmniOutliner"
    writable document types
end tell

This will return the list of UTIs, assuming you're running it from an AppleScript editor.

org.opml.opml
com.apple.rtfd
com.omnigroup.omnioutliner.oo3
com.microsoft.word.openxml.document
com.omnigroup.omnioutliner.oo3template
com.omnigroup.omnioutliner.oo3template-package
com.omnigroup.omnioutliner.oo3-package
com.apple.iwork.keynote.key
com.omnigroup.omnioutliner.plain-text.fixed-width
public.rtf
public.plain-text
com.omnigroup.OmniOutliner.WordExport.MSWordHTML

Though I just noticed this isn't returning a fully correct list, it's missing the HTML options and has some we removed. For HTML you would use:

com.omnigroup.OmniOutliner.HTMLExport.HTMLDynamic
com.omnigroup.OmniOutliner.SimpleHTMLExport.HTML