I'm also having this problem and it's driving me crazy. I want the game to always use the same vertical resolution, then use the ratio of the screen to determine the horizontal resolution (in landscape mode). Then the game should be zoomed in/out to fit the full screen. Since the initial resolution from flash.Lib.current.stage.stageWidth is a little less than what it should be because of the Android navigation bar that auto-hides, the game has a thin black bar on the left and right sides of the screen. I then try to resize the game to full screen shortly after it starts (since the ratio will be correct then), but I've not been able to do this without breaking something.
The closest I've come to solving this is by first calling "FlxG.scaleMode = new StageSizeScaleMode();" shortly after the game starts, but then FlxG.width and FlxG.height will be wrong (with the screen resolution I think), so I hacked a way to change just FlxG.width and FlxG.height to the values of FlxG.camera.width and FlxG.camera.height (which for some reason are correct). FlxG.resizeGame() would not work like I wanted, the game would not be zoomed to fit the screen.
This seemed to work, but has an issue. If I quit the game via Android navigation bar, and open it again (so the game resumes), FlxG.width and FlxG.height will have the screen resolution dimensions, so the positioning of elements will be incorrect (since I use FlxG.width and FlxG.height to position things).