Just one year after that paper claiming the DNA half life of 521 years[1], the DNA of horse from 700k years ago was sequenced [2]. That would be about 1344 half-lives. Then, in 2021 the DNA of a mammoth that lived 1.2 million years ago was sequenced.
To answer your question, dinosaurs last lived 65 million years ago.
Dinosaurs (non-avian) lived 66 million years ago+. The conditions that can preserve DNA longer is cold which is why Mammoth DNA in permafrost was able to be recovered. There's no permafrost from 66 million years ago. There's no means by which pre-avian dinosaur DNA might be preserved.
What about the Michael Crichton "mosquito stuck in amber" idea? I've been curious about that for ages - assuming the amber is room temperature, would that even help preserve DNA for an extra day? I've been leaning towards "no", but I am extremely far from an organic chemist!
Encasing in amber really only shields you from outside things. Those include chemicals (especially oxygen, oxygen is _very_ reactive), life (bacteria) and possibly some shielding against radiation (eg light).
Those do encompass a _lot_ of the reason that anything decays, but unfortunately it's not _all_ of the reasons things decay. And over millions of years, the remaining decay mechanisms are enough that you're really not going to have much/any intact DNA. It makes for a good story though.
To answer your question, dinosaurs last lived 65 million years ago.
[1] https://www.nature.com/articles/nature.2012.11555
[2] https://www.nationalgeographic.com/science/article/130626-an...
[3] https://www.science.org/content/article/mammoth-molars-yield...