HI, I'm Dr Steve. I am sorry to hear about your goat.
Without examining him it is hard to know for sure, but from your description of his actions, one possible could be overeating. This ia also called enterotoxemia. It is caused by a growing lamb eating too much grain at one time. In some cases it is not the actual amount of grain eaten, but just eating more than he is used to can cause this problem.
When a lamb eats more grain than it is used to, the pH changes in the rumen and causes an acidic environment, this allows bacteria called CLostridium perfringens to overgrow and produce a toxin that gets absorbed into the blood stream and gets to the brain. THis causes the staggering he is doing.
Kicking with the back legs can be due to pain in the rumen and intestines and the gut being sucked in can also be a symptom. The treatment for this needs to be done as soon as possible to be the most effective and is usually best done by a vet. It includes giving antitoxin to neutralize the toxin in the blood. Giving sodium bicarbonat IV and orally to neutralize the acid buildup , giving activated charcoal orally to absorb any toxin in the rumen before more gets into the blood stream and giving penicillin to kill the clostridium perfringens. I also give dexamethasone IV to help prevent laminitis in the hooves.
Another possible cause of these symptoms could be a urethral calculi. This is a bladder stone that becomes lodged at the end of the penis and prevents him from urinating. This cause the bladder to fill and cause back pressure on the kidneys. This can be fatal, ( and so can the enterotoxemia, by the way) if not addressed as soon as possible, THe treatment for this is trying to squeeze the end of the penis to break up the stone. THis is not very effective and most lambs have to have the penis amputated. Of course this is also best done by a vet. If you have seen him passing a normal stream of urine , this is not very likely, but if the urine just dribbles out or if you have not seen him urinate, then this may be his problem. He may kick with the hindlegs as well with this condition. In some cases if you hold the lamb by th head, clamp his mouth shut with oyur hand and put another hand over the nostrils thus preventing from breathing for abot 3- seconds, when you release your hands, some lambs will urinate. If he urinates and looks normal, then he is not likely to have this problem. IF he strains and does not urinate or only dribbles, then he is probably blocked. Again both of these problems need a vets attention and the sooner the better.
There can be some uncommon neurological diseases that can also cause staggering like rabies ( keep your hands out of his mouth) wear gloves if you try to hold his mouth to get him to urinate just to be safe. Some bacterial infections, especially brain infections can cause these symptoms, but the first two I mentioned are more common in my practice. I hope this has helped and was not too late. If it has would you please rate my answer. I will check in the morning (US time) to see if you have more questions. THanks for the question.