Something Parker did

I disagree, in that his terror was more than appropriate (I know you made note of this) given what he both witnessed as well as experienced, and to feel anything less would take away from the authentic feel which all of the characters portrayed throughout the film. In other words, who wouldn’t be taken aback by seeing an alien for the first time, let alone third time in Parker’s case and in a matter of hours at that and all that had transpired regarding the horrific nature of each occurrence.
Feeling terror or fear does not equate to cowardice. Some people fight and some people engage in flight, no judgment either way, but Parker was a fighter through and through. And I don’t think he went back into the vent to retrieve the flame thrower, he went back into the vent to help/save his friend, most likely with the knowledge that there was nothing left of Dallas to save and that going in would probably cost him his life as well.
Let’s not forget he did not hesitate to save Ripley from Ash’s attempt to murder her as well as attempting to save Lambert’s life as well, going so far as to tackle the Alien when Lambert was frozen in fear.

In the novelization, the crew finds a big hole in the vent, where the Alien ripped through, and carried Dallas away to its lair. Parker claims the flamethrower was the only thing he found around the hole - no body, no blood, nothing else.

That implies he did not go into the vent, he could see the hole and investigate the surrounding area.

In the movie of course we don't get such indication of a hole, so we can assume Parker entered the vent briefly, and it is in character for him to do so. After losing Brett, he wanted to grab every chance to save someone else. Maybe hoped the alien only wounded Dallas so he can still be retrieved, etc. Point is, they knew exactly where Dallas went missing, he could have been in and out of the vents in a few minutes.

Later on, we get clear evidence of him trying to engage the alien in hand to hand combat when Lambert is in danger. So for the viewer it's like "hey, he had to go into the vents himself to retrieve the flamethrower" - but then comes the realization of "well, he's tough and charges head first into situations, so of course he did".

All in all, there is nothing wrong with that, he knew exactly where he wanted to go inside the vent, and could do it quickly. Also, the xeno did not wait for him, because it had to "store" Dallas in its lair - as we saw in the deleted cocoon scene. Of course he couldn't have known that, but he trusted his own flamethrower, and I can even imagine him going into the vent, fueled by his need for revenge over Brett and Dallas (and Kane of course).

Yes, he was terrified, but basically he is a tough guy - it's not mutually exclusive for people to have conflicting feelings about the same thing you know :-)

I've always noted that he says "We found this lying there," implying that he didn't go in alone.