Because the guy who owned the domain wouldn't sell it and we loved the name. Dropping the "e" was Caterina Fake's idea — I was against it at first because it looked so wrong, but I eventually came to see the wisdom: it was easy for us to get the domain, but it was also more distinctive & recognizable, easier to search for, etc.
Bonus story: for a long time when I searched Google for "flickr" I got a "Did you mean flicker?" suggestion. I knew we'd have "made it" when that stopped. Eventually that message did stop showing up … and by 2005 or 2006 the search results page even asked "Did you mean flickr?" when searching for "flicker". That's when I knew it was big! (Google seems to have stopped doing that since.)
Why did Flickr drop the "e"? (en)
At Quora to the question : Why did Flickr drop the "e"? Stewart Butterfield, founder and former boss of Flickr answers :