This study did not demonstrate that RNA from current vaccines is integrating into our DNA. However, they did demonstrate, convincingly, that there is a viable cellular pathway by which fragments of SARS-CoV-2 viral RNA could integrate into our genomic DNA.
https://elcolectivodeuno.wordpress.com/2021/02/19/study-finds-it-possible-that-rna-from-an-mrna-injection-can-be-integrated-into-our-dna/