Great!

I realize they are only static constants, but do you want to add redirects from the old location to the new one just to assist people learning the new locations? Like this: https://github.com/FlixelCommunity/flixel/blob/dev/src/flixel/util/FlxU.as#L397

Though, the code needs to be modified slightly for constants (it's actually a getter that looks like a constant, I love how you can do that in AS3):

/**
* Path behavior controls: move from the start of the path to the end then stop.
* 
* @deprecated This property is deprecated. Use <code>FlxPath.FORWARD()</code> instead.
*/
static public function get PATH_FORWARD():uint
{
    FlxG.warnDeprecated('FlxObject.PATH_FORWARD', 'FlxPath.FORWARD');
    return FlxPath.FORWARD;
}

Sure! I forgot about that. As soon as I have some time I will add them.

I've added the deprecate warnings and tested the code. It looks good to me. It's good to merge.