When inserted properly, you shouldn't be able to feel FLEX disc at all. Discomfort is likely caused by FLEX disc not being inserted quite right.
Next time you go to insert it, make sure you are pushing the edge that goes in first DOWN toward the floor and pushing it along the bottom of the vaginal canal. This way, it sits at an angle and fully covers the cervix. Then make sure the front edge (that goes in last) is tucked above your pubic bone and pushed past it as far as it can go.
Everyone's anatomy is different, so it can definitely take some time to get the hang of using FLEX, so don't be afraid to take your time to figure out how FLEX works for you.