I have been having random luck with the flash player running in Chromium on my Lubuntu computers. I have 5 different machines and two of them refused to run flash. Any time I went to a flash enabled website the plugin would crash.
After reading this website I checked out chrome://plugins but only saw one instance installed. I tried disabling that instance and the crashing would stop but the site would then tell me I needed to install the plugin. I tried making it ask me before running, and it would ask, then crash.
Finally I tried going to chrome://plugins and expanding the details and disabling the flash plugin from there, even though it seems to do the same thing as disabling it without the details open, the results are different. If I disable the main plugin for some reason it still doesn't work, but going into details and disabling it there fixed the issue.