For new, un-used/un-worn fabric, I would think you would be ok with air-tight storage, as long as the container (plastic of some sort?) doesn't out-gas some kind of vapor, or leach some kind of chemical compound into the fabric directly (or into the trapped air space), that could cause harm to the fabric over the long term. I would wrap the fabric in some kind of fabric-safe tissue to prevent direct contact of the fabric with the plastic, and periodic inspection of the fabric to ensure no long term surprises.

For things like finished kilts that have been worn, I would recommend a good professional cleaning (or thorough wash, rinse, and dry) first, and then a full day or two to air out before placement in the container, so that cleaning agents, or evaporations from sweat and body oils, don't get trapped in the container.