I don't knit - only crochet - but it amounts to the same thing. I always block my crocheted blankets, whether they have any actual wool content or not.
I used a large board cut specially for the purpose. I covered it in 1" thick foam, and then covered that with a checked poly-cotton (for helping with measurements) and stapled it all on the back. Not particularly pretty but it does the job.
I use - literally - dozens and dozens of pins, pinning every inch round the edge of the blanket. I use long pins and angle them at about 30 degrees into the foam. It takes a while but using so many pins eliminates the frilly edge issue.
If the yarn has a wool content I use a wrung out pressing cloth and lightly steam it, moving the cloth when dry and re-wetting it frequently. If the yarn is acrylic, I just hover the iron about an inch above the work, and let the steam do the work. Allow to dry, and it's done, but I don't remove the pins until the work is cold and dry.