The developers are looking into this to see if there's anything they can do to help with the issues members are having with adobe's latest update. Some players have reported that, saving and refreshing every few farms has helped them, perhaps try that or working offline. May or may not help differs from person to person.
Hi there, Chrome uses it's own built in flash player and updates itself, so I'm not sure what flash player you have been downloading, possibly one for another browser. If you have another browser you can use, try un installing chrome and download a new copy.
Happy Farming 
we all are addicted to farmtown!! (and most of us are more than a little nuts, too!!! lol) 
