Speech and language therapist. (SLT) Not all are feeding specialists though. Dd2 had SLT from birth (which was kinda bizarre) but obv nothing to do with actual speech (that was later lol). A good SLT will probably be able to get a good idea from assessment (they basically just watch you feed them) and may see if a swallow study is needed.
As a thought (something else for you to try anyway) we had to put food into the sides of dd2's mouth (she has really crappy oromotor) in order for her to be able to feel it/ move it (bizarrely, despite 3 or 4 years of brilliant SLT - where we had been doing this for years, we didn't work out until she was 4 that she had no lateral tongue movement).
There are lots of exercises you can do - I really like the website www.new-vis.com
(We used it with a toddler/ pre-schooler rather than a baby, so not sure how useful it is yet - the 'feed your mind' section was our go to. Interesting stuff. Our SLT suggested it as a source years ago)
I give you that for interest only - it's obviously aimed at much more involved children, but you might be able to have a think and see if anything sounds familiar.
NHS dietitians are shit for kids with feeding issues that are related to oromotor skills. I went once and never went back. To refer you to a dietician because he is losing weight is too simplistic. He's losing weight because for whatever reason, he's not swallowing the food. The best they could do would be to suggest different textures, and in my experience that's easy enough for anyone with half a brain cell to try - and you probably already have.
Dd2 found more solid textures easier (she struggled with thin liquids/ purees, and it was impossible for her to cope with mixed texture baby food - like that baby pasta in a sauce, for example.) so we added thickener to everything and out it in the side of her mouth so she could get a grip of it. (Obv with her oromotor, she couldn't handle stuff sloshing about as her tongue couldn't manipulate it to form a bolts, as belle said)
No need to freak out though - dd2's issues were well documented all the way along - she was tube fed and no gag reflex. We already know your chap has a good gag reflex and by the sound of it, a really good regurgitation reflex 
Dd2 would do the barf thing too, later, especially with unexpected textures. So essentially, the first mouthful was always the one that was going to shock her system and get thrown back up, and then after that it was as if her body was able to recognize what was coming and hopefully deal with it better. (Our rule was three spoonfuls - if none of them stayed down we gave up, but usually by that point she had worked out how to deal with it).
We had SLT advice all the way though. In discussion with SLT we avoided a swallow study (they aren't particularly nice and we didn't want to trigger any avoidance issues!) it was pointless as we pretty much knew what was going on anyway. We had a repeat prescription for antibiotics that we could always access at the doc, because we got to be able to tell when she had an aspiration level choke and gag, rather than a 'normal' gag and clear. so we would just go and get the anti-bs and wait for the chest infection to start, rather than hassling the doc every time.
The paed will refer to SLT. We barely saw the gp as they were terrified of her. I'd walk in, in tears about the feeding (for three months she could only drink at night, as her muscle tone was so high during the day that she couldn't coordinate a suck and a swallow, so I spent most of the time like a zombie trying to fit in all the feeds at night) and they would just send us straight to the hospital. They had no idea what to do with her.
It's become clearer over time what her issues are, and you'll be pleased to know that since about 4 she has managed pretty ordinary food, so even for crazy kids like mine it does get better!
Get thee to a decent feeding SLT.