What do you want to do with the GFX100S? Only JPEG photos ? Only RAW photos ? Only videos ? all together ? Do you want to do image editing and video editing with layers? Without further information, this becomes a guesswork.

Thinking about the 100S. Read you need a lot of capacity for the large files. What would I need? Thank you    

Then you would have to know at what frequency the display runs from the mobile phone. Modern mobile phones have significantly higher frequencies than 60Hz and are able to generate variable frequencies, depending on the application. Then there is the problem with polarization. If you can adjust the shutter speed on the camera directly, you should choose a synchronous shutter speed. As an alternative, you can use another mobile phone model. With my Samsung Galaxy S10+ DUOs, I don't have these problems with the Fujifilm X-A1.

Yes.  Excuse the quality as I have had to reduce it from 4K Dscf7475-40.3gp

Do you have an example video?