Kershaw now has 45 strikeouts since his last walk-but is it a record?

No, not according to Tom Ruane. See Most Strikeouts Between Hits Allowed... And Then Some.

Here are the best streaks that he found from 1956-2010:

Pitcher           SO  IP    Start         End

Curt Schilling    56  44    2002- 5-13    2002- 6- 8  

Greg Maddux       53  71.2  2001- 6-20    2001- 8-12  

Pedro Martinez    49  42.1  2000- 8- 2    2000- 9- 4  

Dennis Eckersley  47  51.2  1989- 8-22    1990- 6-12  

Koji Uehara       46  38    2010- 7-19    2011- 4-15

John Smoltz       45  39    2003- 7-24    2004- 6-11  

Eric Gagne        43  29    2002- 5- 4    2002- 7- 3  

Javier Vazquez    43  54.2  2005- 4-25    2005- 6- 9  

Bret Saberhagen   41  47.2  1994- 5-10    1994- 6-13  

Greg Maddux       41  51.1  1995- 6- 3    1995- 7-13  

Luke Gregerson    41  33    2010- 4-14    2010- 6-20

 
Tom posted an update on the SABR list and gave me permission to post it here. He looked at more years:

I re-ran the query from 1946 to 2014 and Curt Schiling is still at the top.

The current top ten list:

Curt Schilling         56  44.0 2002- 5-13    2002- 6- 8

Greg Maddux            53  71.2 2001- 6-20    2001- 8-12

Pedro Martinez         49  42.1 2000- 8- 2    2000- 9- 4

Dennis Eckersley       47  51.2 1989- 8-22    1990- 6-12

Koji Uehara            46  38.1 2010- 7-19    2011- 4-17

Craig Kimbrel          46  27.0 2012- 5-20    2012- 8- 2

John Smoltz            45  39.0 2003- 7-24    2004- 6-11

Eric Gagne             43  29.0 2002- 5- 4    2002- 7- 3

Javier Vazquez         43  54.2 2005- 4-25    2005- 6- 9

Cliff Lee              43  31.2 2013- 9-11    2014- 3-31

Sorry for the poor formatting (there's a reason why I usually only post

links to these sorts of things). Each line contains the players name,

length of streaks, innings, start and end date.

The leaders by decade:

Craig Kimbrel          46  27.0 2012- 5-20    2012- 8- 2

Curt Schilling         56  44.0 2002- 5-13    2002- 6- 8

Bret Saberhagen        41  47.2 1994- 5-10    1994- 6-13

Greg Maddux            41  51.1 1995- 6- 3    1995- 7-13

Dennis Eckersley       47  51.2 1989- 8-22    1990- 6-12

Fergie Jenkins         39  43.1 1971- 7- 6    1971- 7-28

Don Drysdale           37  51.1 1962- 7-13    1962- 8- 7

Robin Roberts          30  40.0 1955- 6- 5(1) 1955- 7- 1

Luke Hamlin            22  37.2 1940- 8-30    1940- 9-15(2)

Hal Newhouser          22  18.1 1946- 9-18    1946- 9-29

The 1940s leaders are only complete from 1946 to 1949.So far, Dazzy Vance

has the highest mark from the 1930s:

Dazzy Vance            41  42.0 1930- 9- 2    1930- 9-27(1)