The hadith in question can be found, via multiple sahih chains of transmission, in the Sahihain as well as in the lesser Sunni collections, with slight variations in wording (Muslim 55:7504 & 55:7506, Bukhari 447447 & 28122812, Tirmidhi 3826, etc.). The authenticity of this prediction is well-established, and considered unassailable by Sunnis.
While none of the above narrations make mention of his last provision (whether it was milk or not), they clearly report that the prophet predicted Ammar's death at the hands of a rebellious group (فِئَةٌ بَاغِيةٌ), who would "invite him to Hell-fire."
It is established that Ammar died during the battle of Siffin, and the above report was presumably referring to some soldiers of Muawiya's army that opposed him. In his Sunan, introducing the section entitled "The Virtues Of 'Ammar bin Yasir" (13/11), Ibn Majah reports thus:
...[Ammar] met his martyrdom at the age of 93, in the year 37 AH, at the hands of the Syrian army.