Getting the MStar/SigmaStar chips is pretty difficult but not impossible. Note that most of the chips seem to have a minimum order quantity of 2080 so if you want less than that you will need to find someone that is selling left overs.
This is a list of brokers in/around China that have been used to source parts. Being in this list is not a recommendation in any way.
Since some sites reported on the Breadbee the MSC313E is available on ebay.
The MSC313 and MSC313E sometimes appear on TaoBao. At the time of writing the SSC325 is available from numerous sellers. The SSD201 and SSD202D is also availabe.
Seeedstudio sells a system-on-module featuring the SSD202.