Hi again, mate!
Here is the fixed file: https://drive.google.com/file/d/1_8AKEZZvarJSb89moiEdEe9QM_NREFef/view?usp=sharing
The problem was that you are using Movie Clip Symbols as masks and these Movie Clips tend to loop like crazy during the runtime even though they have only one frame inside. So, for some reason, this creates those problems. Could be screen refresh or something else, I'm not sure exactly why.
To fix the masks, the only thing I had to do was change the Instance Type to Graphic in all keyframes on the timeline.
Then I stopped them, i.e. chose Single Frame from Looping Properties.
The fastest way to achieve this was to unlock only the mask layer. Then I activated Edit Multiple Frames spanning All Frames; Selected All and from Properties changed the Instance type to Graphic; then chose Single Frame.
That's all. Mask works as it should.
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Just one more note: Never use Movie Clips in non-interactive projects. For character animation only use Graphic Symbols. They give a lot more control over what you do.
Good luck!
Nick - Character Designer and Animator, Flash user since 1998 | Member of the Flanimate Power Tools team - extensions for character animation