My contribution to this is based on 20 odd years, very odd years, welding. My scars include a third degree patch on the ankle and numerous ouchies over my bod. And I've done pioneer village blacksmithing.

Wool would be better than acrylics, a leather apron is best and commercially available.

Wool under coverall has a value except it can trap gases which makes it a bomb. Butane lighter horror stories, gas leaks, add to the caution tale.

We used cotton and went to nomex coveralls. Cotton smolders but will ignite. Socks catching fire inside the boot is a rare treat. Elbow burn came from buddy putting out fire on elbow by pressing into me, "no, no, pull away." I wasn't even burning at that point, just starting to be aware of it, it's a welder thing.

Nomex is lighter, radiation burns happen and there are little melt holes all over my clothes. Sometimes the sparkies get through but they're cooler after that. Cooler means little dot burn instead of big burn. Yes, I wear golf shirt and long nomex pants under the coveralls, most of us do, many have long sleeved shirts.

The sport kilt site has a photo of a farrier working using their product, can't remember if he is using an apron.

Myself, if I was going to smithy work and wanted to wear a kilt, I would talk with Robert at R-kilts and see about his canvas/duck product. It's heavy duty. Historically, a wool kilt must have been used but I think that's an awful expense for something that will look terrible within months. And I would get a commercial leather apron. I can't see any maker coming close in price. The aprons are fairly wide for more coverage and the ones that cover the trunk can be folded down for more coverage or cut off. (Got to assume this is your own forge, can't imagine any employer letting you in wearing a kilt. I'd have trouble getting to my locker on the floor and would have to use a separate entrance most likely.)