I can't give an exact date on this for two reasons. First, the Brooklyn Public Library has wonderfully digitized the Brooklyn Eagle, but 1901 is as far as it goes. Second, the Brooklyn Historical Society's Library has been closed for renovation for years. It's due to re-open in the fall of 2004.
It's not clear when this was called "blackout." Perhaps it was sold as "chocolate layer cake" for some time before the name was thought of. The New York Times has a few citations for Ebinger's, but the coverage of Brooklyn is pitiful. It will have to do for now.
14 May 1942, Maryville (MO) Daily Forum, pg. 3:
BLACK-OUT CAKES.... 35c
The VAVRA BAKERS
THE SOUTH SIDE BAKERY
4 September 1945, Wisconsin Rapids Daily Tribune, "In Hollywood" by Erskine Johnson, pg. 8, col. 4:
Before leaving New York, Carl Post met SUsan Hayward and asked her if there was anything he could do for her in the big city. "Yes," said Susan, mouth watering, "bring back a chocolate layer cake from Ebinger's Bakery in Brooklyn." Post brought the cake and started back to Hollywood by plane. But the temptation was too great. He ate the last piece over Salt Lake City.
10 November 1961, New York Times, pg. 40:
Ebinger's Bakery Started in 1898,
With German Pastry as a Specialty
(...)
It might be said that Ebinger's grew up with Brooklyn. Arthur Ebinger's parents, who has come here from Germany, opened their first Brooklyn bakery on Flatbush Avenue in 1898.
(...)
Chocolate cakes, incidentally, are on of Ebinger's best sellers in stores patronized largely by Jewish people.
4 December 1968, New York Times, pg. 43:
Blackout Cake
(Waldbaum's supermarket ad--ed.)
27 August 1972, New York Times, pg. 19:
Tears Replace the Coffee Cakes
On Ebinger Bakeries Final Day
30 August 1987, New York Times, pg. L.I.31:
You bought a blackout cake: a rich chocolate layer cake filled and frosted with dark fudge and dusted with chocolate cake crumbs. It was named for the wartime blackouts (but, if it had been fed to the enemy, it could have ended World War II two years earlier).
10 July 1991, New York Times, pg. C10:
"Ebinger's is back!" I cried.
...she always brought a stack of green and brown boxes from a wonderful bakery called Ebinger's.
Inside one of those boxes was always a blackout cake.

