Can I use amaranth flour or another grain flour as a substitute for white flour in tortillas?

You might try to add some amaranth flour or any other kind of flour, but it's difficult -impossible I think- you can make a bread or a tortilla out of 100% amaranth flour. Wheat flour (that you call "all purpose white flour") contains gluten, that is functionally used to make dough stick together. If you use amaranth, rice or other kinds of flour you'll find that it's difficult to make the dough.

If you want to make a healthier tortilla use whole wheat flour, and add whatever you want inside: amaranth, sesame seeds, linseed, nuts, peanuts, almonds, etc.

I've been to a restaurant which proposes pizzas made of 100% of amaranth. So it is definitely possible to make some kind of dough, although I'm not sure how much complicate and lengthy it can get.

You would probably have to nixtamalize most gluten-free grains and pseudocereals (including amaranth) in order to use them successfully in tortillas if you don't want to add gluten. These doughs from nixtamalized grains are known as masa. Corn is usually used for this, however, but other things are possible. You can buy masa harina, which is dried and powdered masa de maíz (which is masa from corn) at the grocery store and make corn tortillas with it. If you use regular corn meal, it will probably fall apart and be grainy (or else thick like fry bread).

'… nixtamalized amaranth flour can be used to replace maize for tortilla production.' This is an excerpt from Pseudocereals and Less Common Cereals: Grain Properties and Utilization …, edited by Peter S. Belton and John R.N. Taylor (p. 236). So, yes, what you suggest is possible, although it might take some learning and time. Companies should really sell masa from all kinds of grains and pseudocereals, although advertising it to people who don't know what it is might be the hard part. They could call it tortilla flour, I guess (but I imagine there are many more uses).

You would probably need to nixtamalize the amaranth before grinding it into flour, however. That's how it's done with corn. So, I wouldn't buy amaranth flour for this purpose.

Nixtamalization may make the food more nutritious in certain ways. It does for corn, anyway. I'm not sure about amaranth.

Other gluten-containing grains (e.g. barley, rye, kamut, spelt) might be workable for tortillas, but likely not as ideal as wheat flour, without some kind of process like nixtamalization.

Apparently, you can make tortillas with oat flour, with a very simple recipe.

FYI: Oats don't contain gluten. However, they are often contaminated with it (hence gluten-free oats being sold particularly) and they contain a similar protein called avenin. Even with gluten-free oats, avenin can cause issues for people who need a gluten-free diet if they haven't been on the diet for a certain amount of time.

You can even make a flour from wheat that has been nixtamalized: Masa de harina de Trigo. I imagine it's even easier to make tortillas with it than with regular flour (however fine or white it is).