almond and coconut flours won't thicken like flour. They may end up being kind of gritty. There are lots of low carb alternatives to thickeners but nothing is exactly like flour. Some low carb flours have thickening properties, like Lupin flour and soy flour. I hate the taste of soy flour, but YMMV. Lupin flour tastes ok-ish to me.

I usually pour some of the soup (sans meat, if you can) into a blender and blend it until thick and smooth, then pour it back. That'll thicken things up.

Low carbing means changing life long habits like having perfectly authentic gumbo, or whatever. Just need to adjust to your new reality. I had to give up all wheat/barley/rye products when I was diagnosed with a gluten issue. It was tough at first, felt kind of sorry for myself, but I got used to it.