Could you use old fashioned oats instead of quick oats or oat flour?

You can easily make quick oats out of regular whole oats, by buzzing the regular oats for a few bursts, in a food processor.That way, you can achieve whatever the recipe author had in mind.

Yes, you could definitely use old fashioned oats! I prefer quick oats because they absorb the liquid from the egg and honey more quickly, and therefore the dough is a bit more homogenous. Old fashioned oats will keep their more distinct texture within the dough, and to make up for the slower liquid absorption, it might be helpful to let the dough rest in the fridge overnight before baking.

Yes, old-fashioned oats should work.