There is no homemade micarta. There are homemade laminates that are often called things like Mycarta. Micarta is a registered trademark and is a phenolic laminate. You can't make phenolic laminates at home.
That said, many people have made laminates using burlap. The resin will be absorbed into the fibers, so any dye in the resin will be in the fibers.
Use the best and hardest grade resin you can get. Use a slow set hardener. I recommend West System 105 resin and 206 or 207 hardener.