I am not a lawyer, but I am not sure what "MP3 and MP4 natively without proprietary codec" means. Those codecs are proprietary, so you must have a license for them. It does not matter whether you use open source implementations of encoders or decoders for them, because the technology itself is patented and needs a license in order to be used (decoded or encoded).
So the answer is probably no.
Regarding Flash, if Adobe provides a download of Pepper Flash (so not one you get from a Google Chrome installation), you can make Chromium work with it, using some command line flag(s). Search the group (or the web) for ways to make it work - it has been discussed several times. I believe it would be a legal thing to do, but, again, I am not a lawyer.