This rare kanji has no clear standalone meaning. Treat its meaning as uncertain.
箞 combines 竹 (bamboo) with 卷 (roll/scroll), suggesting a bamboo-related object that can be bent or rolled. The exact historical development is uncertain.
Bamboo 竹 over a scroll-like shape 卷: imagine bending a bamboo strip into a curved scroll. The reading たわ.める means to bend or flex something.
For ケン, picture Ken bending a bamboo strip into a scroll: Ken -> ケン, and the bamboo flexes under his hands.