I was wondering about this as well. I was hoping someone would reply to this thread with a solution, but that never happened. So I solved it on my own instead :P
It appears as if IE just won't run the game if there is no .mp3 version of all sound files. This is a problem even if you haven't added any audio, since HaxeFlixel includes two sound effects (one for button clicking, I believe, and the jingle played in the splash screen).
You could manually add .mp3 version to the export folder, but there's a better way – HaxeFlixel actually comes with mp3s already (for Flash), they're just not included in the html5 export. So simply open Flixel's include.xml file, find the assets node for mp3s and change if="flash" to if="flash || html5".
I'll make a PR to fix this. It would be nice if we could m4a instead of mp3 to avoid licensing issues, though, but that would require changes to openFL, which apparently doesn't allow m4a.