Kind of late, but I thought I could be helpful on this topic. Using only these three ingredients, I've done some math and and figured out where the nutrients are particularly deficient. Barley is the best of these three grains in terms of ratios of protein and nutrient density.
For a mix with the proportions of:
Barley: 75%
Oats: 15%
Rye: 10%
The resulting levels of vitamins and minerals are:
Protein: 61.119%
Fat: 109.433%
Calcium Ca: 0.921%
Copper Cu: 44.17%
Iron Fe: 56.86%
Magnesium Mg: 193.6%
Manganese Mn: 66.140%
Phosphorus P: 110.96%
Potassium K: 216.9%
Sodium Na: 4.833%
Zinc Zn: 70.357%
Vitamin A: 5.866%
Vitamin D: 0%
Vitamin E: 20%
Vitamin B12: 0%
Thiamin: 421.214%
Riboflavin: 50.240%
Pantothenic acid: 276.05%
Niacin: 403%
Folate: 117.8%
Arginine: 59.628%
Histidine: 109.5%
Isoleucine: 44.969%
Leucine: 70.131%
Lysine: 43.621%
Methionine: 52.600%
Phenylalanine: 92.100%
Threonine: 56.330%
Tryptophan: 84.937%
Valine: 56.600%
As you can see, it's impossible to create a mix that's balanced out of only these three grains. You'll need to provide a source of calcium and protein for sure. If you're able to feed fish of fishmeal pellets at a rate of 15% of their diet by weight, that would bring the protein content to 18% and provide a variety of vitamins that are difficult to obtain from vegetarian sources, such as Vitamin D. I've calculated a much more balanced feed using ingredients that should be readily available to most people:
Barley, raw, pearled: 50%
Rye: 15%
Oats: 10%
Fishmeal (or other protein source): 15%
Leafy greens: 5%
Oyster Shell: 5%
Basil: 1%
Ginger: 1%
Cilantro: 0.5%
Brewer's yeast: 0.5%
Cayenne, pepper: 0.5%
Spearmint, dried: 0.5%
With the above mix, the resulting vitamin and mineral levels are:
Protein: 103.447%
Fat: 130.536%
Calcium Ca: 69.726%
Copper Cu: 55.555%
Iron Fe: 193.653%
Magnesium Mg: 316.929%
Manganese Mn: 78.156%
Phosphorus P: 257.951%
Potassium K: 330.446%
Sodium Na: 161.633%
Zinc Zn: 102.549%
Vitamin A: 259.518%
Vitamin D: 109.999%
Vitamin E: 116.7%
Vitamin B12: 125%
Thiamin: 361.857%
Riboflavin: 114.576%
Pantothenic acid: 353.257%
Niacin: 524.108%
Folate: 157.44%
Arginine: 140.975%
Histidine: 240.676%
Isoleucine: 101.947%
Leucine: 149.598%
Lysine: 148.571%
Methionine: 135.498%
Phenylalanine: 152.430%
Threonine: 131.708%
Tryptophan: 128.874%
Valine: 118.677%
Let me know if there are certain ingredients you want or needed to include, or could not gain access to. I can recalculate the nutrient levels. I'm a programmer and wrote a script that allows me to calculate it easily. I can also explain how I calculated all of these numbers, if you were curious.
Hope it helps