I haven't figured out every single clue, but I'm pretty sure you are
I am connected to pressure,
Much like what I am behind,
As air passes through them whichever;
I think this is referring to the lungs (air passes through the lungs, transferring oxygen to the blood) but I'm not altogether sure.
Greatest when keys are combined.
No idea what this is about. [EDITED to add:] It turns out -- see OP's comments -- that this is the bit for which it's relevant that your skin is in some sense your largest organ. When you combine keys with air passing through pipes (I confess I don't really see what "them" is referring back to, or what "whichever" is doing) you get a (pipe) organ, and "what I am behind" (the skin) is the "greatest" (= largest) organ.
I am connected to flow.
Blood flows through your circulatory system.
Never am I in a glass.
No idea what this is about. (It's certainly possible to put blood in a glass, and of course there's e.g. the Bloody Mary cocktail...) [EDITED to add:] OP explains in comments that since drinking blood is a bad idea, you wouldn't put it in a glass. Which indeed you wouldn't, but I bet someone has at least once :-).
At sight of a vampire, go!
Their teeth look at me and surpass.
Vampires are bloodsuckers, and if you saw one and knew it for what it is you would probably pale (the blood leaving your face) with fear.
I remain blue, red or green.
Blood is actually red. The nobility are said to have "blue blood", supposedly because their indoor lifestyle would have given them more visible veins, which appear blue by contrast with the redder surrounding flesh. There is an extremely rare medical condition in which blood turns green; I don't know whether that's what the last bit of this is about, though.
Or sometimes I may turn to violet.
There are some marine animals with violet-coloured blood.
Nin, bin and then for marine,
Scientists end with the triplet.
Nope, can't parse this. [EDITED to add:] OP explains in comments that this is alluding to haemocyanin, haemoglobin, and the fact that it's marine animals that have green and violet coloured blood. (Sulfhemoglobinemia was not in view here after all.)
When drank I am toxic, believe it or not!
Yup, drinking blood is not a good idea.
But without me, eventually, you will start to rot.
It won't take very long.
My vowels come once in the place of a winner.
Perhaps because the only vowel in BLOOD is O, and there is exactly one O in PODIUM, or in GOLD. [EDITED to add:] OP explains in comments that "in the place of a winner" means "in the word formed by the first letters of the lines", that word being IMAGINATIONS -- which is another word with exactly one O in it.
The rest win in breakfast, lunch and dinner.
The consonants are B,L,D, the first letters ("winners") of those words.
Water is thinner.
Old proverb: "Blood is thicker than water".