The Online Etymology Dictionary has a citation a little earlier than the OED:
Phrase everything but (or and)
the kitchen sink is 1944, from World War II
armed forces slang, in reference to intense
Out for blood, our Navy throws everything
but the kitchen sink at Jap vessels,
warships and transports alike. [Shell fuel
advertisement, "Life," Jan. 24, 1944]
I'm not sure if these are definitely examples of the phrase or coincidental, but here's some earlier quotations.
The Washington Times (Washington D.C.), February 20, 1914:
Having "blown in' his sav
ngs on a complete new set of scenery,
Jerry was logged out this day like a
circus horse. He had on everything but
the kitchen sink and the door mat.
New-York Tribune, February 19, 1919:
We Sell Dependable
Merchandise at Prices Lower Than Any Other
SiSre. but for Cash Only
Store opens 9:00 A. M.
and closes 5:30 P. M.
| Pots and Pans!
To say nothing of rolling pins, clothes bask
ets, wash boilers, per
f. colators, casseroles,
I towel bars, cloth venti
lators, china, cut ^lass,
earthenware well, in fact everything but the
kitchen sink is included