I use L-glutamine for my ulcerative colitis (which I believe is linked to leaky gut), and it is the only supplement I have ever taken where I actually noticed a night-and-day change in my symptoms. In just a few days, my bowel movements will go from soft to formed, and sometimes I can get myself out of a mild flare (bloody diarrhea, cramping) by taking glutamine. My boyfriend calls me a canary in a coal mine because my gut is so sensitive that I can be his radar as to what foods, restaurants, etc. are good or bad. My quick response to the glutamine supplement tells me that it truly works, and for those with more "silent" symptoms of leaky gut, I can confidently say that glutamine is absolutely worth trying.
I use glutamine powder (don't use the capsules, you won't get a high enough dose), 1 heaping teaspoon (5 grams) mixed in my Nalgene bottle of water once daily. I sip on it throughout day and it works just fine for controlling my symptoms. If I'm having a flare or more severe symptoms, I will take it 2-3 times a day.
For those really interested in learning more about
leaky gut, I would highly recommend listening to Alessio Fasano's talks on YouTube like
this one. I firmly believe that leaky gut and the gut microbiome are going to be the future in treating many chronic illnesses and autoimmune diseases, and Alessio Fasano is one of the pioneers in this movement. Note: his focus is more on the role of gluten in leaky gut and autoimmune disease, but he also elaborates on many other interesting concepts.