No idea about if they're the record, but assuming it's either last season's Chelsea or the 04/05 version,
Last year's Chelsea did the double over 12 teams, everyone besides Swansea, Liverpool (Chelsea only took 1 pt from Liverpool), Arsenal, Spurs, Burnley, Palace, and the rags.
04/05 Chelsea did the double over 12 teams as well, everyone besides CITY (Chelsea only took 1 pt from City), Villa, Spurs, Bolton, Arsenal, Birmingham, and Newcastle.
So to break the record (assuming it is 12) of doubles in a season, we need 11 wins out of the following games:
Newcastle H, WBA H, Burnley A, Leicester H , Arsenal A, Chelsea H, Stoke A, Brighton H, Rags H, Spurs A, Swansea H, West Ham A, Huddersfield H, Southampton A.
Last year's Chelsea did the double over 12 teams, everyone besides Swansea, Liverpool (Chelsea only took 1 pt from Liverpool), Arsenal, Spurs, Burnley, Palace, and the rags.
04/05 Chelsea did the double over 12 teams as well, everyone besides CITY (Chelsea only took 1 pt from City), Villa, Spurs, Bolton, Arsenal, Birmingham, and Newcastle.
So to break the record (assuming it is 12) of doubles in a season, we need 11 wins out of the following games:
Newcastle H, WBA H, Burnley A, Leicester H , Arsenal A, Chelsea H, Stoke A, Brighton H, Rags H, Spurs A, Swansea H, West Ham A, Huddersfield H, Southampton A.