ANSWER:

No, It is not permissible as it includes shirk and exaggeration in praising the Prophet salla Allahu alaihi wa sallam.

https://islamqa.info/en/answers/115502/qaseedat-al-burdah-by-al-busayri-and-an-explanation-of-what-it-contains-of-kufr-and-heresy

QUESTION: Can we recite or listen a poem praises the prophet saw called Qaseeda Burdah