That’s not how it works. All birds share a common ancestor that was a cousin to it, so they’re all equally related to it in terms of when they split off. For chickens to be more closely related to T. rex, they would have to share a more recent common ancestor with it than they do with other birds. That would also make T. rex a bird if you still wanted to count chickens as birds.
Feel free to cite your source. If you're thinking of the idea that chickens may have more conservative genomes than most other birds, then I get where you're coming from, but we don't actually know what T. rex's genome looked like to be able to compare them. It's entirely possible that the T. rex genome would have changed in a lot of places where the chicken genome is relatively conservative, making chickens no more similar to T. rex genetically than any other bird is. That aside, all birds evolved from the same node on the cladogram, which was already pretty far removed from tyrannosaurs at that point. Saying chickens are more closely to T. rex than other birds are would be like me saying I'm more closely related to my great uncle (whose DNA we do not have) than my biological sibling is because I have 25.01% of his brother's - my grandpa's - DNA and my sibling only has 25%. It's not provable because we will never recover the DNA to know the overlap. Even if we could prove that, it would only demonstrate that we are more related in a very strict genetic sense and ignore that we are exactly as related in terms of shared common descent.
You have very fair points, but I do have a small amount of hope that one day we could find or recreate usable T-Rex dna.
Yes, I know that DNA degrades relatively quickly, and finding DNA more than a hundred thousands years old/ 1 million years old is incredibly rare, but I remember reading that in some edge cases that DNA has been found in cases of 1 million or 10 million years old, and around a decade or more ago, it was reported that possible cellular structures that may contain T-Rex DNA had possibly been found.
I wouldn't get my hopes up, and there are hundreds of potential problems though.
I'm not a paleontologist or geneticist though.
