When a pattern tells you to use either DPNs or a circular needle, they are telling you that you can use whichever of those two methods of circular knitting. Both DPNs (Double Pointed Needles) and circular needles can be used to knit mittens in the round.
I don't think I've seen a pattern for mittens that is knit flat ... but I haven't really looked for one either, so maybe someone else here on KH will know of one for you.
