I was suprised to learn how expensive flex PCB is. In my experience, roughly five times more expensive.
My typical, small, rigid board costs on the order of a few dollars for three. My first flexible PCB board was over twenty dollars for three (although it was about twice as large as my typical board.)
One issue is that a flexible board is more likely to have wasted space, that is, the bounding box (for which you are charged) is larger than the actual board area. A flexible PCB is liable to have dangling parts, or extensions, where you might ordinarly use wire cables. Such things will increase the bounding box.
The board of this project had extensions in four directions. The bounded area was fifty percent waste: 6 areal units of waste, 6 areal units of actual board.
If your use case is: just need the lightness, don't need the extensions, then the cost differential won't be as great.
You can panelize your board (tile a plane, bin pack) to reduce the waste.