The rubbery texture can be from over-kneading when combining the burgers. For some recipes, I have pre-baked at a low temperature then grilled to get the right texture on the outside. This would work with a recipe with a resting period as well as one that just dries.
Also, if the egg replacer is not binding correctly (I am assuming you are using Ener-G), try using a chia or flax egg (1 tbsp of either milled, then combined with 3 tbsp water and set to congeal). This will raise the moisture in your patty, which likely already has a good amount based on your recipe, so you can use other wet ingredients instead of adding water.
These are two related, but different products.
Gluten is protein that is formed from two pre-cursor proteins, glutanin and gliaden, found in wheat flour in the presence of water and under enzymatic activity.
It forms resilient stretchable networks which give yeast raised bread its structure.
Whole wheat flour is... well... whole wheat berries, ground up. It is mostly starch, but contains all glutenin, gliaden, and the necessary enzyme to create gluten, which forms naturally when the flour is moistened, if given long enough or kneaded to accelerate the process. However, even a very "strong" flour (bread flour) will have no more than about 10%-15% percent protein by weight, so it cannot form more than that amount of gluten.
Vital wheat gluten is essentially concentrated, powdered gluten, without the rest of the parts of the wheat berry.
They are not freely interchangeable, as the gluten does not bring the starch, bran, and other components that flour does. You may, in specific recipes, be able to use just gluten, but not in the general case. And even if substitution is possible, you would have to determine the correct ratio to achieve the desired outcome.
Using vital wheat gluten in lieu of whole wheat flour, in most applications, will either fail completely (no thickening from starch, as in a gravy), or be dense and rubbery, and practically unpalatable (as in a bread).
Best Answer
I've never found wheat gluten flour that was higher than 80% gluten which is what I use, adding some when I make bread with rye flour. But if you can't eat wheat due to high fructans content, would you still be able to digest the fructan in the other 20%? You wouldnt be adding much gluten flour so the small amount of fructans might be okay.
Rather than buying and using standard gluten-free flour which is quite expensive, why not mix up your own? It's easy to. I've made gluten-free bread a few times for a friend who's since moved. The wheat-free flour mix that I made was rice flour, tapioca flour, potato flour and coconut flour in the ratio 3:3:3:1. You can then add gluten flour to this mix if you still want to try using gluten instead of xanthan gum. Xanthan gum is added to all gluten-free bread flours to help the dough keep its shape while rising. It's not needed if you plan on adding gluten though.
Bread flour is normally 10-13% gluten. Trouble is I don't know if that's by volume or weight. Maybe someone reading this knows and can tell you. If it is by volume, then replacing 2 tablespoons of the flour mix with 2 tablespoons of gluten flour should give you roughly the right gluten content. Hard to be exact as it's possible gluten flours vary in their actual gluten content.