I was able to do this with native api calls. My solution worked perfectly on my machine. Here is what I did:
First, get Microsoft Process Explorer. Using this tool, I was able to get the flash plugin dll's name that chrome uses which is called pepflashplayer.dll in my case.
Next, a little search on Bing got me this article. It's C code so I converted to C# and after some coding I was able to retrieve the correct Chrome process ID that uses flash plug-in.
I have uploaded my solution to SkyDrive for you to check here. Note that I am not closing any handles in my sample so you'll have to add that for a real project.
There might be better solutions out there but this one should work. Hope it helps.