Even if use flannel sheets try these
Pill Free Double Knit Crescent Cover 5 Pack Natural Color
I'm a big fan of the No Pill sheets. 15 washings & no pilling so far. And even more of a fan of these cradle covers. I use them with my remaining flannel, which I am phasing out. Even if u like using the flannel sheets, I recommend these for the face. No, or minimal pilling; smooth against the face AND DON'T HOLD OIL SMELL & LAUNDRY SOAP. The face cradle is the most important part of my table. I use an upgraded / best cradle; Memory foam cushion; & smooth, stain free cover w/ no oil or laundry smell, so I can sent lightly w/ essential oil. Tip: Turn inside-out b4 laundering to further protect against pilling. If ur flannel has any smell, use 2+ cups white vinegar in HOT water wash (nothing else) to strip the oil and detergent from them. Then Oxy w/ minimal detergent going forward.