How to install a flush mount LED light over an old square recessed box?
I have installed a couple of those flat panel LED’s. I would go with that one. 

The one I installed had some slots in the panel for screws, you would mark those locations on the ceiling and then drill and install anchors so that you could screw the panel to the ceiling into those anchors. 

This one does appear to have a mounting plate  that attaches to the box but because the plate  is so big you could just  drill holes in the plate  that would line up with the ceiling joist  but it’s not a heavy light  so some good quality anchors would be sufficient if you can’t lineup with a joist .