"Assigned to" does not show up because it is a column type of "People". Currently people/lookup/choice columns are not supported so they will not show up.
From another thread:
08-11-2016 04:38 PM - Flow Staff
"Flows can indeed be used to both create and modify SharePoint list items, however currently Lookup, People, and Choice columns cannot be written to. Today we only support reading from them, so they can be used as dyanmic outputs in other actions. This is a known limitation that we will be addressing soon. "Assigned to is a "People"
Another Option:
You could add another column to use instead of Assigned to that is of the text type and use it instead and just hide the assigned to column. We just created one called "Assigned Staff" and write the vaule to that instead. It won't have people picker functionality if you change it from the sharepoint side, but it worked for what we needed to do.