Hi, I did a pair of Fingerless Mitts double knit a while back as well. You can see the in-progress image below. Anyway as for the thumb and fingers go (I only had the thumb, but you get the idea) I simply would knit the parts for the thumb and fingers onto seperate dpns and work them normally. And for adding a new color I'd add it in to both sides. Since doing the FM you'd have two strands, one for each glove, you would need to add in the new color for each side as well.
Yeah I knitted the FM double knit, but inside out. It was easier to keep the strands seperated that way, instead of moving it back and forth. The inside glove was Knitted, while the outside glove was Purled. This kept the strands in back and in front of the work at all times, so easier to keep them from getting tangled.