Poster is asking for an integer value of MS since Epoch, not a time or S since Epoch.
For that, you need to use NOW(3)
which gives you time in fractional seconds to 3 decimal places (ie MS precision): 2020-02-13 16:30:18.236
Then UNIX_TIMESTAMP(NOW(3))
to get the time to fractional seconds since epoc:
1581611418.236
Finally, FLOOR(UNIX_TIMESTAMP(NOW(3))*1000)
to get it to a nice round integer, for ms since epoc:
1581611418236
Make it a MySQL Function:
CREATE FUNCTION UNIX_MS() RETURN BIGINT DETERMINISTIC
BEGIN
RETURN FLOOR(UNIX_TIMESTAMP(NOW(3))*1000);
END
Now run SELECT UNIX_MS();
Note: this was all copied by hand so if there are mistakes feel free to fix ;)