How to create a seamles UV map for an hexagonal grid texture? I have very little experience unwrapping UVs. I'm not able to wrap my head around how to seamlessly create the texture for a beveled rectangle.

Here was my attempt when UV unwrapping it. I ended up with large, ugly seams. 



In Rocket League they not have seams, but their texture was not a simply repeating hexagonal pattern like mine was. Theirs was filled with irregular sized hexagons, as well as pentagons in some places where the pattern needed to transition and curve. 



I'd love any direction as to how you think the developers might have accomplished this seamless, custom UV texture.
I haven't played RL in a while, but are the ceilings the same beveled rectangle shape?

It looks like your images are being stretched as they get closer to the beveled edge.  It also looks like your screenshot isn't from Blender, so I don't know how to do it in whatever software that is, but if you're working in Blender I'd suggest going to UV mode and adjusting the vertices until it looks better.  Also, check your texture and see how the edges line up at the top/bottom and left/right.  It might take some photo editing and/or scaling to get it to work.

Good luck!