is Killua truly jealous of Palm?
Yes, I absolutely think he is!
It's never explicitly stated, but the subtext is so in your face in a few different ways that it's essentially not even subtext any more.
Togashi could have chosen so many different ways to portray the way Killua feels about the Gon/Palm date subplot, but making it clear over and over again how bothered Killua is by the whole situation absolutely reads as jealousy, especially within the larger context of the arc. Look at these especially!
Togashi puts so much emphasis on Killua's expressions and distress throughout the whole subplot. Of course it's partly intended to be comedic, but this situation with Gon and Palm does have serious emotional weight for Killua as well--pulling out the needle, his breakdown in front of Palm, what she ends up saying to him after that, etc. I do think the exaggerated and extreme ways Togashi expresses Killua's feelings are intended to make the audience go, "Oh, he's really jealous, isn't he?"
People can argue Killua's reactions are just because of who Gon is on a date with (someone unhinged/violent and much older than him), or that it's just "concern" about Gon because of his nen situation, and those are both definitely aspects of what's going on here--but to reduce it down to only that ignores those deeper emotional impacts it has on Killua. I think the protectiveness aspect is something Killua uses to veil some of the other things he's feeling about it even though of course he is legitimately protective of Gon in this situation (and he has good reasons to be so). I also think Togashi himself uses the ambiguity to his advantage here, because if he put in romantic jealousy that was any clearer, would Jump allow it?
The way Killua goes immediately from the topic of going on dates/being freaked out about the prospect of Gon having been on dates before to feeling heartbroken because he wants to be with Gon forever the next panel is telling, in my opinion... (The English translation is a little vague, seems like it was intentionally toned down. In the original Japanese version he says he wanted to be with Gon forever.)
Here's a post where @tjlnn22 and I discuss this weightlifting scene in more detail.
I firmly believe that a big part of Palm's role as a character is to get the audience to question the nature of Killua's feelings for Gon. Without considering this context, the way her character is set up from the beginning and what role she's intended to play in Chimera Ant Arc is confusing. But when if you look at her character as having been built for that role, suddenly her entire character and subplot makes sense. Here's an older post where OP talks about some of the framing of Palm's character, and then I talk in more depth about why Palm is written the way she is.
It especially makes sense when you consider that the date with Palm is one of the factors that destabilizes Killua's faith in his relationship with Gon, leading to him wondering if they're acting together as friends or just as teammates. Here's an awesome post @tjlnn22 put together and submitted to me on this topic, with specific details supporting this argument. I think this is an important part of the arc that gets overlooked, and I love how clearly it's laid out in the linked post.
Killua also acts dismissive of Gon worrying about Palm to the point where other characters comment on his behavior, which to me seems like another sign of jealousy and bitterness on Killua's part. Then when he encounters Palm again after her transformation, this is how he behaves towards her:
Hands on his hips, full sass mode here. Again with the jealousy...
...And then shortly after this he proceeds to have a total emotional breakdown when he admits to himself that he thinks maybe Gon cares more about Palm than him, and that Palm might be the only one who can help Gon, rather than Killua. Of course there are more factors than this behind his breakdown, including him getting pushed away by Gon prior, but this is DIRECTLY the thought that leads him to start crying and then sobbing on the ground.
The Palm subplot is one of the biggest things in the series that makes me confident that the romantic subtext around Killua's feelings is completely and utterly intentional. The way the whole subplot is constructed, the decisions Togashi makes around Palm and how she's presented as a character, the way Killua's reactions and emotions are emphasized with regards to it, and the significance of this subplot in the greater arc of Killua's character all show a great deal of thought and care, and it's hard to come to any other conclusion when looking at it carefully.
Thank you for asking!
