Maybe you've figured out a workaround in the meantime, if not, here's a way to do it.
Create an additional column in your SharePoint list of type single line of text.
If your person column is "AssignedTo", name the new column "AssignedToString" or the like.
Create a Flow triggered by "When an item is created"
Action "Update Item"
Populate AssignedToString field with AssignedTo.DisplayName
Now you have a text field containing the AssignedTo person's name and can thus include it in the Search function
Search(DataSource,TextSearchBox1.Text,"AssignedToString")
I've done this for multiple person fields in a list, e.g. AssignedToString, ProjectManagerString, ApproverString with the result that a user can search for a fraction of his name and will see all records where he figures in any of these roles.
I've as well used it for the ID of a record. so that in the same search box you can enter the ID and find any matches. Not very elegant because searching for 12 will not only return 12 but any ID containing the string "12" (123, 312, 3125, whatever).
I think date fields can be dealt with in the same way, but an exact date will have to be entered as search term, as otherwise the results will be quite ambiguous (03/20 for example could return 03/20/2018 but as well 05/03/2018.
Please let me know if this helps.