Yes, this is gluten free
Potato, tapioca, cassava, arrowroot and the nut flours are gluten-free plants, and these are what gluten-free baking is actually built from. Same caveat as the grains, for the same reason: almond flour and chickpea flour are frequently milled where wheat is also handled, so on a flour the certification is doing real work the ingredient name cannot do.
flax is covered by CiCi's entry on gluten-free starches and flours, which share this answer and the reasoning behind it.
Every one of these is the same ingredient. The number of names is a large part of why gluten slips past people who read every label.
Point CiCi at the barcode on the product you're holding and get this same reasoning in about two seconds, plus the carbs and the full nutrition panel. 360,000+ packaged foods are already read and waiting.
This answer comes from CiCi's ingredient lexicon — the same rules the scanner uses, not a separate article. Where reputable sources disagree, CiCi takes the conservative position and says so.