My hunch is that this is a classic case of doing very low carb (VLC) without sufficient prep. If you do VLC cold turkey, your stool will become dry as rocks and your colon will lose moisture. It will be like trying to give birth to jagged pieces of rock.
You have to go VLC gradually. Immediately add back some safe starch: in your case, sweet potatoes or white rice. I would add about 250g of sweet potatoes or yams to start. Portion control if you have to if you have BG issues.
Ask your bro if he has any moisture in his colon: he can tell you immediately. Most people who are constipated say they're constipated, but they should be able to give you relevant details. Is it Bristol chart 1? Zero moisture? You have what Paul Jaminet calls the "danger of VLC diets" or what Konstantyn calls "fiber menace", i.e., doing Atkins without sufficiently preparing yourself for the smaller, denser stool resulting from a high-fat/low-carb diet.
Solution: add back starch. If you have to VLC, do so gradually. Slowly decrease your starch intake. Otherwise, stay above ketosis by doing about 100g of carbs.
Btw, most Asians aren't supposedly gluten sensitive to the degree caucasians are. But if you're confirned as being so, then it's likely that your bro also is.
Also, don't do VLC and then all of a sudden start eating 3 packs of Shirataki or Konji noodles or 3 avocadoes in a day. The sudden influx of fiber and mass will just overwhelm your colon, resulting in fecal impaction --- that's actually worse in many ways than just a case of bloody stool. Been there done that.
Lost of water, yes. But beware, lots of coffee and tea could also dehydrate you and worsen your constipation or fecal impaction.
Another thing he can do is use suppositories for the interal fissures/hemorrhoids he presumably has. Get some hemorrhoid cream for the ousdie and apply every morning to the outside and inside. If his skin is dry, also apply some moisturizing lotion to his buttocks. This should take care of the internal and external hemorrhoids and will stop irritating the hemorrohids in a week or so.