I searched in Bing using the term Hankie quilts and found several fun examples. You could make a woman's body on the top and then use the scarves as the skirt, letting them hang free. Some cute ideas here for storage that could be converted to a quilt idea.
https://hative.com/creative-scarf-st...display-ideas/
Another idea would be to make a large Dresden Plate using pieces of all the scarves. Or how about a Southern Belle quilt block but leave the skirt as 3D?
https://www.bing.com/shop?q=southern...28A1FC7C0A6261
Or, you could just pick a block pattern and make every block a 2 color block with the same background and a single scarf featured for all the colored pieces in each block. Float the blocks with background fabric for the sashing to give definition to the blocks. This Pinterest page has several good ideas. Stars of different colors would work well.
https://www.pinterest.com/anniesews/two-color-quilts/