You need to use a beta version of Flash Canvas:
The creator of Flash Canvas is very responsive by the way and helped me solve this. Here's what was recommended and what I did that solved it:
Basically you load all your images into the Flash Canvas using loadImage(), which is a method added to the latest beta of Flash Canvas. And then in the callback of the last image loaded, load C2. C2 will load, and be injected into the swf, and all images will be drawn without causing flickering because they are already cached in the swf by the loadImage() method.
Next, there is a few issues with easing in flash canvas that must be solved. But overall, we're finally pro.