The relevant Delta website page is here:
https://www.delta.com/content/www/en...-partners.html
It should not be difficult to get the benefits when flying DL, just make sure your VA number is on the itinerary, and it is mostly automatic. The only issue I've had is SkyClub access at some obscure locations, they might need some assistance explaining that you have access on a domestic itinerary (regular DL Platinum members don't even get this access, but VA Platinum do).
I've never had to carry any documentation with me to receive my benefits, but it isn't a bad idea I suppose.