Ok I have been nosing around on the internet and found a few things for you to look at:
Week 10: Cancer & Raw Diets, Early Vaccination, Reflux, Roundworms, Immune Health, Treating Allergies Holistically | Dogs Naturally Magazine
Fresh food and meat based. As simple as possible. No fillers. Ideally, gluten free (check the Honest Kitchen ingredients). I find eggs to often work wonderfully in this situation and many consider them to be nature’s perfect food. If he can tolerate them that is. I suspect that you have already tried many foods, but novel proteins are often best. Rabbit, venison, pheasant, etc. Avoid foods with high histamine levels. This includes many fish like tuna, mackerel, amberjack, etc. Also avoid high fat foods that will slow emptying of stomach contents and may predispose him to reflux.
Need some ideas. Dog has severe acid reflux. - The Shiba Inu Forum
As far as diet, we tried raw. Emma was the worst on beef. Through research, I learned that Acid Reflux is due to either too much fat and protein in the diet or not enough. For Emma, it was too much, so we went to raw turkey. It was Small Batch which is an organic and free range recipe. She did better, but still had problems. We tried yogurt - wasn't enough. We tried goat's milk - not enough. She is currently on Honest Kitchen Zeal (fish - low protein, low fat).
Our solution: We have been working with a chiropractor for a few months now on other issues Emma has (she has many). Our chiropractor started us on a new supplement: Sulfurzyme. It is all natural. Emma has been on it for a while and doesn't vomit, doesn't burp, doesn't chew on her paws, doesn't lick the wall, and doesn't take pepcid any longer.
Ottawa Valley Dog Whisperer : Acid Reflex, GERD in Dogs, Cats - Natural Remedies, Causes, Symptoms
Very good article
Dr. Jean Dodds' Pet Health Resource Blog | Raw Honey: A sweet food for the health of your pet
Another good article on Honey
The Benefits of Feeding Your Dog Green Tripe - Spotless Dog Wash
Raw green tripe is beneficial to dogs suffering from digestive problems, sensitive stomachs, food intolerance and even leaky gut syndrome. In non clinical trials, a regimen of six days of using raw green tripe as 25% of a raw fed dog’s diet have shown marked decreases in acid reflux and irritable bowel symptoms.
The Stink On Tripe | Dogs Naturally Magazine
I am NOT brave enough to try raw Tripe. I do give my kids this and they love it. I only smell it when I first open the bag not why they are chewing on it. It has helped improve everyone's teeth and I do not see upset stomachs etc.
Barkworthies - Green Tripe Sticks (7oz) - Barkworthies
Remember every baby is different so it is going to be a trail and error for awhile. I had to keep a log with Huly and watch him with different foods etc. I would only add one new thing at a time where I knew what might set him off. It could take him up to 48 hours to show an allergy or disagreement with a food. (his was mostly allergy issues)