white silk, fine silk, gauze
紈 centers on fine, delicate white silk fabric, especially gauze. The idea is a light, smooth, and refined textile.
紈 combines 糸 (thread/silk) with 丸, which likely contributes the sound and possibly the idea of something rounded or smooth, fitting the fine silk meaning.
The left side 糸 is thread or silk, and the right side 丸 looks like a smooth, round ball. Imagine a ball of fine, white silk thread that is light and gauzy.
For カン, picture a can of fine white silk thread: can -> カン, and the silk is so delicate it fits in a can.