Like any other bug, feather mites can travel and you don't need to have pet birds, hens or anything else around for them to arrive and start eating your fletching feathers. I go trout fishing and do my own fly tying using feathers so know what a problem they can be.
You don't need to buy nasty chemical sprays to get rid of them. Whenever you buy feathers for fletching, or ready cut feather fletchings, you should put them in an airtight zip-lock poly bag and put them in the freezer for a couple of weeks. The little blighters and their eggs can't survive that. When you take the bag out keep it closed and only open when you need to get feathers out for fletching. If you add new feathers to the bag, put it back in the freezer for a couple of weeks to avoid fresh contamination.
If the fletchings on your arrows are being chewed, strip them off and refletch. It is probably worth using a spray on your quiver and the equipment box where you keep your arrows to get rid of any infestation.
And we thought the only mite we had to worry about was when might we get a six gold end!