The CW released its spring schedule including the date for the season finale for Supernatural.
From Entertainment Weekly
The season finale of SUPERNATURAL will air Thursday, April 25 (8:00-9:00pm ET/PT).
Also, carrying forward the current schedule of aired episodes, the 300th episode, which will the episode 13 of the season, should air on February 7, 2019.
* Timetable reprinted from http://www.thefutoncritic.com/showatch/supernatural/listings/
Will keep you up to date as we get more information.