There is a history article [1], but essentially, the founding developer made the MTASC AS2 compiler back in the day before making Haxe, and the SWF target (AVM bytecode) was the first target Haxe supported. To this day it remains popular with the 2D games market (ex-flash). The OpenFL [2] framework promises (with mild success) to give you the Flash API with the Haxe language on native targets. So flash still is part of the Haxe community, though less and less it involves the actual Flash Player runtime.
Personally I do web development in Haxe, using Neko or NodeJS on the server, and JS on the client. I've toyed with the Java and C++ targets, but so far haven't had a single project which compiled to Flash. I find the language on it's own has a lot of features that are appealing outside of the flash environment.
1: http://haxe.org/manual/introduction-haxe-history.html
2: http://www.openfl.org/