Ibn Abbas (may Allah be pleased with him) narrated the Prophet (peace and blessings be upon him) drank some milk then called for some water. Once he got the water he rinsed his mouth then said, “It has fat.”
Recorded by Bukhari 211 and Muslim 358
Benefits for this subject:
Imam An-Nawwawee said,” This hadeeth confirms it’s recommended to rinse the mouth after drinking milk.”[ Sharh Saheeh Muslim ]
Shaykh Al-Uthaymeen said, “The reason why the Prophet (peace and blessings be upon him) rinsed his mouth was because of the fat. It can be understood from this action that it’s legislated to rinse the mouth from all foods which contain fat, regardless whether drank or chewed. Its good manners to rinse the mouth afterwards to remove the fat. If the substance is heavy in fat, then it’s better to use siwak. For this reason the scholars say: it’s sunnah to use siwak to remove any fat after eating if the smell of the mouth changed.
(Sharh Saheeh Al-Bukahri)