ANSWER:
Qaseedah al Burdah is filled with shirk and not permissible.
https://islamqa.info/en/answers/115502/qaseedat-al-burdah-by-al-busayri-and-an-explanation-of-what-it-contains-of-kufr-and-heresy
https://islamqa.info/en/answers/115502/qaseedat-al-burdah-by-al-busayri-and-an-explanation-of-what-it-contains-of-kufr-and-heresy