You could try soaking it in water with 20 mule team borax....1 cup of white vinegar in your washing machine cycle may work...

I bought fabric, books and such from an estate sale. The home didn't smell of smoke but most likely that was due to the weather and open windows for the setup and sale. Got home and opened trunk-UGH! Carried it around the back of the house and put on patio. One batch at a time went into laundry tub with vinegar- 3 cups into half full tub OVERNIGHT. The next morning drained the tub, added laundry detergent and swished- soaked 30 min. Then drained and into washing machine for a wash with oxyclean added. Took care of the smell! Good luck!

ammonia.
if you can set the water level in your washer, highest level.
if you have one of those stupid new washers that won't let you decide, then fill the bath tub and let it soak for a few hours.
the odor of the ammonia is horrific, but does wash out completely - along with whatever smell you were trying to get rid of.

I will give all the above suggestions a try, starting with fresh air and progressing from there. I am apt to believe that the issue is with the glue or whatever was used with the "flocking" however as it makes sense that that is what was washing out and is causing the odor. I've washed a ton of old fabrics, some of which I'm sure were exposed to smoke at some point in their lifetime and haven't noticed the same issue. I will also research doing a burn test and see what comes of that.

I'm wondering if what you have is a bonded fabric from the late 60s/ early 70s. Frequently fabrics had a thin knit fabric bonded to the main fabric. My wedding dress was bonded crepe. Gave it more body/stability. May also have been intended as a drapery fabric originally.

Ozium is the best I've found to get rid of odors. My firefighter son told me about it. After I wash a fabric, if it still has odor problems I just lightly spray it with Ozium and walk off and leave it. When I come back in a little while, the odor will be gone.

This was an ad on my Quilting Board site when I opened it today: "vamooseproducts.com". You might want to go to that site to check it out. The product is "Vamoose" and comes up when you open the site. Hope it helps.