What fatoldladyinpjs said. Another thought, though...
I just saw a fingerless mitt pattern online that starts in the round, but when you get to the thumbhole, you work in rows for a bit then go back to working in the round. Since you're working in stockinette, that flat edge may well roll a bit like the other ends will. If you go with this method, you'll want to alternate knit and purl rows to stay in stockinette.
Have fun knitting your mitts, and please do let us know how they turn out. We'd love to see them!
"Knit on, with confidence and hope, through all crises."
- Elizabeth Zimmermann