Narrated Anas ibn Malik: The Messenger of Allah ﷺ drank some milk and he did not rinse his mouth nor did he perform ablution, and he offered the prayer.
Related hadith on this topic
Explanation & Benefits
Shaykh Umar Farooq Saeedi
Benefits and Issues:
It is recommended (mustahabb) and superior to rinse the mouth after drinking milk; however, if one does not do so, it is still permissible.
Source: Sunan Abu Dawood – Commentary by Shaykh Umar Farooq Saeedi, Page: 197