Both my phones are on the same WiFi network and I have NFC turned on for both but what is the qucikest way to select one 400MB file to copy to the S6 through NFC?
For starters, you don't actually copy media using NFC, because the transfer speed (just ~53KB/s) is way too slow to be practical for use in close proximity.1 NFC simply establishes the connection (usually Bluetooth or Wi-Fi Direct) and lets the system transfer the actual file using that connection.
Android's built-in NFC sharing interface is called Android Beam, while Samsung's own take on the feature is called S Beam. The former uses Bluetooth, while the latter uses Wi-Fi Direct, which is up to 10x faster than Bluetooth.2
To share files between two NFC-enabled devices, you should first enable the necessary options in both devices' settings (enable NFC, Android Beam, and S Beam if available). Then go to the appropriate app (in this case, your videos app), browse to the file you want to share, and touch the devices back to back. Tap the screen of the device you're sharing from when it asks you to 'Tap to beam'.
(I have read that S6 devices do not have S Beam in the Settings app, but I can't vouch for that since not many people seem to be complaining about it, based on a Google search.)