I am planning to put the wood medallion with distress engineered wood. Is it possible to do so? and what glue should I use for the border between the medallion and the distress wood?

I don't see why not, but I would send the medallion manufacturer a piece of your flooring first so they can match the color, texture and sheen.

You mean the glue that goes underneath? If so the medallion manufacturer will recommend what to use there.