Should I continue learning ActionScript 3 then slowly adapt to Haxe or just learn Haxe? The problem with Haxe is it hasn't got much support.
If you are using OpenFL with Haxe 3, the vast majority of classes parallel AS3 exactly, so there will just be minor syntax differences. You can usually just use the AS3 documentation to understand classes. Haxe really has matured in the last year.
If you are an experienced developer, I would recommend just working in Haxe. However, if you are new to development, setting up a working environment for Haxe / OpenFL may prove difficult. There are a lot of plates to spin and platform-specific issues you may encounter, so be prepared to need help from forums and user groups.
The setup directions are pretty good: http://haxe.org/download
If you do encounter issues, search here for answers (they're most likely there):
https://groups.google.com/forum/#!forum/haxelang https://plus.google.com/communities/100629265342461903925
If you can get up and running in Haxe, your code will be worth more (since you can deploy to desktop, iOS, Android, HTML5, and Flash) and the skills you development will be worth more (for the same reason).
Good luck!