Selecting files for input Safari applescript

I am trying to automate using Applescript uploading of files to a website. I have gotten to nearly the last step, but can't seem to get a Finder (file chooser) window to respond to scripts.

Here is what the site looks like (i can't give you the actual site, because it is a secure medical record).

The process to upload files is to hit "Add Images" which I can do in Apple/Javascript and it brings up a Finder (file chooser) window like this (again I can only show part because of privacy issues). There are standard "choose" and cancel" buttons on the bottom.

I can't find a way to get this Finder window to respond to Applescript. I have been trying things like:

tell application "System Events"
    keystroke tab
end tell

and numerous others using Finder etc.

Any ideas on how to pick a file out of this window? Or get to this window? Or even find the properties of this window?

Thanks.