Hi @RyanVH,
Is the "Files" a standard table or are you talking about attachments? if this is a standard table there are a number of methods you can utilize to accomplish this.
What I am most familiar with:
1. Create a model driven Power App that contains the tables you are working with or utilize really any model app that already exists in the environment and make sure your user has a role that allows viewing the data from these tables.
2. Utilize Advanced Find in the Model App to select the Files records related to a specific lookup value from the Person table to the person you want. You can add the columns you would like to export etc. here as well.
https://docs.microsoft.com/en-us/powerapps/user/advanced-find

I know the above isn't exactly your situation but similar where I am selecting Opportunity table records where the Account (lookup field on Opportunity) is equal to a specific value. This would be similar for you situation but you would be looking at the Person lookup column on the Files table.
3. Another option is to create a view on the Files table in the dataverse that contains the lookup column for the Person and then all the columns you require from the Files table. You can then add the Files table to your model application and select this view and filter by the appropriate value in the Lookup to the Person you would like.
Hope this helps.
Thanks,
Drew