First lets get on the same page with vocabulary to avoid confusion. There is a feature within Creo called "flexibility" which allows dimensions or features in one model to be adjusted when it's used in another. There is another feature called "Flexible Modeling" which allows you to import from another CAD system and recognize features (such as holes) and adjust them, even though there is no feature tree. It seems you're using the word "flexible" in it's natural sense ("can be bent"), and not referring to either of these feature sets within Creo.
Creo does include a robust mechanism simulation toolkit, that lets you simulate things with real physics, including gravity, friction, etc. This does include adding springs & belts between components. But... It doesn't really show them, the rigid items they're connected to just behave as if they're there. So if you're after a nice looking animation rather than a technical result, this may not be suitable for your purposes.
I have created neato looking animations with complicated flexible components (Storable Tubular Extendible Members, compression springs, clock springs, etc) at various points in the past, but I don't think you'll like how I did it! The shape of the components relied on equations set up in the relations dialog, and could get complicated. Would also include a "VALUE = VALUE + 1" sort of statement, so the motion would increment with each regeneration. Regenerate, screengrab, regenerate, screengrab, etc, and compile animation from the frames afterwards.
You can get fancy with these regeneration controls too. I had a model where I was running these sequences a lot, and going into the relations dialog each time was a drag, so I set up fancy rules. Parameters would have included "ANIMATION_START = YES/NO", which I would just have to flip to start. Other parameters would give the start and stop positions, and increment (or frame rate). The relations included if-then statements which would check the value of the "ANIMATION_START" parameter and do the incrementation if it was set to yes. An "ANIMATION_IN_PROGRESS = YES/NO" parameter was controlled without user interaction, and would set the "ANIMATION_START" value back to "NO" when the increment reached the last desired value.
