When I did these I followed the pattern as written (except for going down a few needle sizes) with Woolease Chunky and they came out very well.
If you want to add a few more rounds between the ribbing and the beginning of the thumb gusset, that would work too. Some mittens I recently knit in worsted wieght had 3 round between the ribbing and the thumb gusset, so you might try that if you’re using a worsted weight or maybe two rounds if you’re using a bulky weight yarn.
I haven’t made flip-top mittens yet, but the mitten pattern I use {FCEK Fall '05} calls for 3 rows worked even for both kids and adult sizes. This is with WW yarn.
HTH,