MyDMX doesn't use chases in the same way as a lighting controller would use them.
The consoles work on a single-step scene based system. This is all well and good provided you can do what you want within those limitations.
Since MyDMX is also scene based, scenes in MyDMX can contain multiple steps, which is more of an equivalent to a chase, but isn't exactly a chase. I don't think it would be entirely possible to convert MyDMX data to a DMX Duo or DMX Partner UNLESS it was the single-step kind of scene, or you want a complicated MyDMX scene broken into multiple scenes and then turned into a chase.
Of course, your best bet would be to have such a package that could do the conversion written or produced by ADJ. Mainly since they have access to the data file formats, it would make sense for ADJ to retain this information internally in order to create such a software application. Of course, it may not possible, but then again it could be.
I think you might want to share a bit more information with how you would want to implement this. It may help people find answers for you, assuming there is a better answer than "no".
The option of releasing tons of information to developers is that it might open up a platform that ADJ might have wished to remain more closed.