Test out if you can directly copy ai files to the clipboard and paste it in flash.
There should pop up a dialogue, where you get 4 options.
The first one will convert the ai to bmp., which you rarely want.
the lower three imports the drawing as vector.
Importing AI files into Flash CC should bring all the images along with it unless the images are renamed/moved. Would like to take a look at your AI file. Could please share it?