To understand why
flashmovie has (currently) been removed from TeX Live, you need to know the policy for inclusion of material. TeX Live is 'Debian free', in the sense that all of the material is available under free-as-in-speech licenses. At the same time, there is a policy of not including code in TeX Live which is itself free but which absolutely requires non-free support material. Sometimes, packages get added to TeX Live which later turn out not to meet the criteria for inclusion, and they are then removed. That does not mean the policy has changed, but reflects the fact that it is not easy to track thousands of separate items. (Note that simply being able to use features from a non-free source is not the issue here, it's requiring non-free support to do anything useful.)
In the case of
flashmovie, Alexander has linked to the start of the discussion about this package. The package itself has a free license, but depends on particular PDF features. While there are a lot of free PDF viewers available, feature coverage varies. In the case of 'interactive' material, life is made complicated as there is a difference between the required feature being part of the ISO PDF specification and actually being implemented by a free viewer. Adobe has added many features to PDFs, not all of which are in the ISO and not all of which are implemented by any other viewer.
Now, not being an expert I am not 100% clear on whether the features required by
flashmovie are (a) part of the ISO PDF standard and (b) available in any free viewer. The latter question seems to be much more complicated than would seem to be the case: there appear to be conflicting opinions!