If the cushion has down in it- and the down in encased in cotton ticking, walk-- the item is already damaged by the fire retardant since the cover is a natural fiber.
If the cushion is just foam then here is the remedy-
I cant believe I'm sharing my secret- but here it goes--
remove the cover from cushion, Zip it back up and sew the zipper tab to fabric to hold it closed temporary while its being washed.
set the cover aside for now.
While your wife is away from house-- clean the cushion in the bathtub.
you will fill up the bathtub with about 20-30 gallons of water-- add 4 oz of dichlor (Pool bleach) and mix until dissolved.-- open windows or exult fan to ventilate. your nostrial should burn, if not add more diclor-- and put on a mask for Christ sake!

Place the cushion in the tub, compress and squeeze the cushion to get the solution deep into the cushion-- let dwell for about an hour.
Drain tub, fill with clean water to rinse cushion using the compress and squeeze step.
once the rinse water has filled the cushion, place the cushion in a garbage bag/or similar. Close the opening of the bag around vac hose connected to your TM or Porty- turn on suction.
this will compress the foam and remove the water. repeat this step multiply times if needed.
Place this cushion is DryRoom/garage with fan, dehue and heater to dry-- in a few hours Water will migrate to the base of cushion near the floor-- extract this water. It might take a day or two to dry.
once the cushion is dry, you can proceed with the washing of the cover.
Wash it in a HE washer in warm water on gentle cycle, If the cover is white use a little bleach. DO NOT put in the dryer.
To insert the cushion into the cover you will use same garbage bag- vac hose technique to compress the foam. once foam is compressed- insert into cover. remove suction, foam will expand. now reach in and start tearing the bag apart to remove.