Remove duct tape adhesive residue from fabric
Goo Gone and similar products work quite well on hard surfaces for removing adhesive residue. You will find that the recommendations for such products also include testing on a hidden portion or similar piece.

It's likely that Goo Gone will work and you may be able to soak the fabric in the liquid to allow better penetration. Once soaked for a while, a detergent wash is likely to be needed to remove the oiliness of GG.

Alternatives to GG include WD-40, with the same oiliness factor, as well as baby oil, mineral oil and peanut butter.

Work the selected substance in the fabric frequently to ensure good distribution.

A quick search using "goo gone fabrics" shows that many posts have been made to indicate the product works on clothing.

Of all the above, I think peanut butter involves the most effort and perhaps the lowest risk of discoloration, but I've never used peanut butter!