I do not think flash MX is available for linux platform. Others i really have no idea.
Actually this may make your life easier....
http://www.pygame.org/
Python is a relatively easy to learn... But, it maybe still too difficult for a 10 years old. But anyway game programming in Linux is supposedly not easy at all.
These day even java can be used to write some cool game. (looks cool, but never play them) Check out
www.java.com