is it too fragile to wash?
i would wash it in the washer- with detergent and white vinegar-
if you want to dry it laying flat---fresh air would not hurt! one of the recommended ways it to lay out a sheet on the lawn- place the quilt on the sheet-then place another sheet over the top of it- to protect it from birds ect
after a while go out & check it- turn it over-
i actually use my hammock= which is a large double one- that way the air flows under & over it- but laying on the lawn- or deck= what ever is doable too- the fresh air certainly makes them nice

vinegar is good for removing odors & softening- mild detergent to help remove the (oily nicotine residue) in the fibers. it is generally not recommended to dry clean them- and often if you take them to a cleaners they do not dry clean them-since they are cotton- they toss them into a large industrial washer- then a dryer- and charge you for cleaning.