Is Blaziken the closest living relative of Tyrantrum?
Almost certainly not; let’s talk about why.
So, assuming that the evolutionary history of the Pokémon world more or less follows the evolutionary history of the real world (which is a big assumption, and we’ll see later why it could easily be wrong), bird Pokémon are the only survivors of the theropod lineage that included Tyrunt and Tyrantrum. Now, strictly speaking, talking about which kind of bird is the “closest living relative” of the dinosaurs is actually meaningless, because in evolutionary biology, how “closely related” two species are depends on how far back you have to go to find their most recent common ancestor, and that will be the same for all living birds; none is more “closely related” to Tyrannosaurus than any other. However, you can reasonably talk about which species are more or less “derived,” that is, which ones retain more of the ancestral traits, and you can talk about which families split off from the basal lineage at earlier points. Like all things in evolutionary biology, no one is 100% in agreement over exactly how the ‘family tree’ fits together, but it’s something like this (from http://blogs.scientificamerican.com/tetrapod-zoology/):
So, as you can see if you look closely, the Galliformes (the order that includes chickens, turkeys, pheasants, quails, ptarmigans and a number of other similar birds) are actually one of the most archaic extant lineages of birds, and by that particular objective metric they are “closer” to the Tyrannosaurs than most other groups, though the Anseriformes, the waterfowl, probably have an equally strong claim. So at this point we have a multi-way tie between Blaziken, Unfezant, Swanna, Farfetch’d, and probably several others I’m forgetting (possibly Psyduck, though he might actually be a platypus and not a duck, which would put him somewhere else completely). But there is actually another group, the branch of the tree immediately to the left of the Anseriformes and Galliformes, with an even stronger claim, and that’s the Palaeognathae, the ratites. This is the group that includes ostriches, emus, cassowaries, rheas, and my own glorious homeland’s mascot, the kiwi, as well as our extinct moa. Are there any Pokémon that belong here? Well, that depends on what you think Doduo and Dodrio are. I think they’re ostriches, which would make them Tyrantrum’s closest relatives if we’re measuring it this way. Jim the Editor thinks they’re an ironic take on dodos, because of the name, which would place them within Columbiformes, the dove family, further down the tree.
Also, shouldn’t we at some point consider Tyranitar as a candidate? Tyranitar is based on Godzilla, which means that he’s sort of one level of abstraction removed from actually being a Tyrannosaur; he also has a weird insect-like pupal stage that’s far removed from anything any known species of dinosaur has ever done. Sceptile also deserves mention, because although he’s definitely supposed to be a gecko, there’s almost certainly some inspiration from theropods in there as well.
And of course ALL OF THAT GETS THROWN COMPLETELY OUT THE WINDOW when you consider that Tyrantrum can actually breed with a number of other extant Pokémon species, most of whom aren’t even birds at all. By any sensible biological definition, two organisms which are reproductively compatible must be more closely related than two organisms which aren’t. And, of course, Pokémon egg groups, although they come much closer to working along biological lines than any other official classification, are still utterly without rhyme or reason in a number of cases (Archeops wHY ARE YOU WATER 3!?), which is why doing the evolutionary history of the Pokémon world is ultimately a lost cause. If you ever sat down to try and figure it out, you would almost certainly come up with something radically different to any reconstruction of the real world’s ‘tree of life’ – if you managed to come up with anything self-consistent at all.
We could, if we chose, try to somehow combine the two approaches, and look for a bird Pokémon that Tyrantrum can breed with. If we do it that way, Tyrantrum’s closest living relative – assuming it’s not Tyranitar – is in fact probably Altaria, the sole avian member of the Dragon group. My logic in coming to this conclusion is methodologically indefensible, but I am sticking to it because nothing else makes sense either. So there.