Create different Final Cut Pro Share Destinations to upload the source edit, ProRes or H.264 to Frame.io. 

In FCP, select the Share Destination Icon, then select Add Destination.
Drag the Export File icon into the list of Destinations.
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Next, choose Action and select Frame.io. If Frame.io is not an option, select Other... and then select Frame.io from your Applications. If Frame.io is not an option, you will need to download the application.

Choose Video and Audio for a mastering format, and then Same as Source or H.264 for the codec. If you are collaborating with work-in-progress files, choose the Web Hosting format and the desired resolution.
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​NOTE: Frame.io supports creating proxy clips for playback with any Apple codec. However, be sure not to use the Format options Apple Devices or Computer. These formats render .m4v files which do not support Timecode track.
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Rename your destination by clicking on the “Export File” title based on your export settings, such as Frame.io H.264, Frame.io Source, etc.