I see no reason not to add the fir bark to your hugelkultur beds as long as there are other log, limbs, etc from other tree species.
Hugelkultur is nothing more than making raised garden beds filled with rotten wood. This makes for raised garden beds loaded with organic material, nutrients, air pockets for the roots of what you plant, etc. As the years pass, the deep soil of your raised garden bed becomes incredibly rich and loaded with soil life. As the wood shrinks, it makes more tiny air pockets - so your hugelkultur becomes sort of self tilling. The first few years, the composting process will slightly warm your soil giving you a slightly longer growing season. The woody matter helps to keep nutrient excess from passing into the ground water - and then refeeding that to your garden plants later. Plus, by holding SO much water, hugelkultur could be part of a system for growing garden crops in the desert with no irrigation.
Fir trees might break down at a slower rate than other tree species:
Pine and fir will have some levels of tanins in them, but I'm guessing that most of that will be gone when the wood has been dead for a few years.
https://richsoil.com/hugelkultur/