Ooh, I've looked for something a little like this! I think I searched for them as "1940s reversible blankets" and then went to "vintage camp blankets". I think they're most known for the Beacon or Esmond labels, though a number of companies put out something similar. Orr is my favorite label for these but I actually don't think they're going to be closest to yours, since they're made of wool and more known for their large scale floral designs. I think Maggie is right and yours might be a cotton or rayon? It looks less dense than the wool ones at least but I'm so bad at looking at something and knowing what material it is! I hope you can really narrow down which material you should be searching for (maybe you should do a burn test on your existing blanket??) because that's what would replicate the right feel.
Esmond might be the closest I've seen to your pattern (although I haven't seen a picture of the whole thing) just because they seem to have done a lot of floral borders with geometric centers. It reminds me of this one in the middle, from
this article:
And I think the texture looks potentially similar, as seen
here:
And like I said, more labels than this have done similar blankets. But hopefully you at least have a couple more search terms to poke around with and see if anything looks familiar! Good luck!!