One of the best things about Captain Jack Harkness as a character is that, from the moment he was first introduced on Doctor Who, he has been challenging any kind of sexuality and gender binary. Even better, he does so in a fun and endearing way that practically no one can resist. When he first appeared in an episode called “The Empty Child” and its second part “The Doctor Dances”, Rose is faintly surprised about how open he is with his affections for pretty much everyone he meets. The Doctor explains “Relax, he’s a 51st century guy, he’s just a little more flexible […] by his time you lot spread out across half the galaxy […] so many species, so little time.” Both the writers and John Barrowman, who plays Jack, have expressed that if any orientation label would even come close to fitting Jack, it would probably be the term “omnisexual”, because, as we see throughout Doctor Who and Torchwood, Jack is literally attracted to any gender, any species, in any time. In fact, in an episode from Torchwood, Jack himself rejects any sort of label, saying “you people and your quaint little categories”.
In terms of a gender binary, you have to hang in there with the sci-fi. Jack Harkness at least seems to be a male human being. However, after the events of series one of Doctor Who, he becomes immortal – which makes him something more than human but not quite alien (and even the alien part is an interesting question, if you view “alien” as “anyone not from Earth”, since Jack is from the Boeshane Peninsula, one of Earth’s off-planet colonies in the 51st century). Further than that, however, it is revealed in series three that he is the Face of Boe who the Doctor meets every so often (and is basically a giant telepathic head in a tank). How that happened and why is still unknown, but the interesting part is this – in an episode of series one, there is a tv reporter that says that the Face of Boe is pregnant. In addition, in the first episode of Torchwood, Jack himself says “still, at least I won’t get pregnant. I’m never doing that again”. This puts an interesting spin on his gender in the series, because (obviously) male pregnancy is currently not possible. More than that, it is physically something associated with females, and Jack has done it. So it raises the question of how sex and gender are classified and especially highlights in a physical way the idea that, rather than a male/female masculine/feminine binary, there is a spectrum of sexes and genders that can’t all be shoved neatly into two boxes.
Jack’s queer time is also interesting to look at over the course of Doctor Who and Torchwood. He grew up in the 51st century and became a Time Agent, until he left to become a con artist. He meets the Doctor and Rose in 1941 and joins them for the rest of the season, bouncing around time and space. After he dies and is resurrected immortal, he uses his vortex manipulator to jump back in time, hoping to get to the 21st century. Instead, he is stranded in the 19th century, where eventually joins Torchwood. When he is reunited with the Doctor, they end up at the end of the Universe. He returns to the 21st century afterward, and joins the Doctor one final time in “Journey’s End”. As explained above, he eventually becomes the Face of Boe and dies for good in 5,000,000,053 (and I did have to look that one up). By this time, he has “died” over 1,000 times and he ages very slowly, so he’s millions of years old.
So why that long explanation? I think mostly to show that Jack’s own timeline, if you will, is actually a big ball of wibbly wobbly, timey wimey… stuff. In other words, queer time, in a physical interpretation. Not only does he deviate from expected gender and sexuality norms, but Jack also deviates from time itself in any traditional sense. He leaves his job to become a criminal, ends up bouncing around to countless different time periods, and he is literally taken out of normative time because he is unable to experience time like everyone else does – he’s immortal and ages extremely slowly, so he lives through centuries without getting older. He doesn’t really “belong” to any one time period and he certainly can’t follow the normative progression of school/work/marriage/children/retirement because he lives too long for it, and given his characterization I don’t think he would choose that anyway.