500 ml of milk a day doesn't sounds so little to me, but I'm not expert to evaluate this. From what you've written, it seems, like he's receiving a normal food, so this is not dangerous for liver.
This is highly specialistic question what you've asked. If you think, you can't get answers from your current specialist, you might want to contact an educated nutritionist - I'm talking about orthodox one. But you should try with your current doctor first.
Barium will maybe show, if there is a problem with GERD, and if any procedure needs to be performed. It looks more like a developmental problem with eating, now they are looking if there are also any structural changes within the bowel. Before going with other more heavy diagnoses, maybe some swallowing tests should be done.
One idea for searching this issue online is, that you connect "chewing" or "thriving" with your suspections.
They said reason failing to thrive is he doesn't eat enough. In 24 hours his total milk intake is 500mls and food is about 10 tea spoons worth stage 1 food is pureed/ soft lumps. he's had a barium swallow test waiting for the results. his milk is infatrini and he has pro-cal additives in it as well.
They should tell you why exactly he is "failing to thrive". "Stage 1 food" - you probably mean elementary diet - is usually used in impaired absorption in small intestine. You have to get information what physical problems were confirmed so far. Long term elementary diet is not good for the liver.