This is a sound and robust chain of transmission, yet none of the major compilers recorded it.
Abū Dāwūd al-Ṭayālisī said: “Jaʿfar ibn ʿUthmān al-Qurashī—who was from Mecca—narrated to us, saying: ‘I saw Muḥammad ibn ʿAbbād ibn Jaʿfar kiss the Stone and prostrate upon it. He then said, ‘I saw your uncle Ibn ʿAbbās kiss it and prostrate upon it.’ Ibn ʿAbbās said, ‘I saw ʿUmar ibn al-Khaṭṭāb kiss it and prostrate upon it,’ and ʿUmar said, ‘Had I not seen the Prophet ﷺ kiss it, I would never have kissed it.’”
This isnād too is ḥasan, and it was reported only by al-Nasāʾī through ʿAmr ibn ʿUthmān, from al-Walīd ibn Muslim, from Ḥanẓalah ibn Abī Sufyān, from Ṭāwūs, from Ibn ʿAbbās, from ʿUmar, with similar wording. Imām Aḥmad likewise narrated this report from ʿUmar in the version transmitted by Yaʿlā ibn Umayyah, and Abū Yaʿlā al-Mawṣilī recorded it in his Musnad via Hishām ibn Ḥubaysh ibn al-Ashʿar from ʿUmar.
We have gathered all of these routes, wordings, attributions, and critical notes in the book we compiled on the Musnad of the Commander of the Believers ʿUmar ibn al-Khaṭṭāb—may Allah be pleased with him. All praise and thanks are due to Allah.
In short, this ḥadīth is transmitted through numerous lines from ʿUmar ibn al-Khaṭṭāb, and—according to many specialists—these routes establish certainty. None of the narrations explicitly state that the Prophet ﷺ prostrated on the Stone, except for what is implied in the report of Abū Dāwūd al-Ṭayālisī from Jaʿfar ibn [ʿAbd Allāh ibn] ʿUthmān, and even there it is not unequivocally raised to the Prophet.
Nevertheless, al-Ḥāfiẓ al-Bayhaqī narrated it through Abū ʿĀṣim al-Nabīl, who said: “Jaʿfar ibn ʿAbd Allāh told us: I saw Muḥammad ibn ʿAbbād ibn Jaʿfar kiss the Stone and prostrate upon it, then he said: ‘I saw your uncle Ibn ʿAbbās kiss it and prostrate upon it.’ Ibn ʿAbbās said: ‘I saw ʿUmar kiss it and prostrate upon it,’ and ʿUmar said: ‘I saw the Messenger of Allah ﷺ do likewise, so I did the same.’”