I don’t know precisely when “Netflix and chill” became a pop culture phenomenon. But like most – or all – phenomena, trademark applications ensue.
In 2015 and thus far in 2016, a fifteen applications have been filed at the USPTO for trademarks featuring “AND CHILL” or “& CHILL.” In all the years before 2015, 43 such applications were filed.
Here are some from the last year or so – click TSDR link for USPTO records:
Note that the application for “Netflix and Chill” is for software for social networking and was not filed by Netflix. It will almost certainly be denied by the USPTO.