I am using rssowl, Version: 2.1.6, Build Id: 2012-12-08 as downloaded from the rssowl.org front page, on Ubuntu 12.04 and my flash is from the Ubuntu repository 64-bit. Everything works ok except that I can't display flash videos in the embedded browser and have to display the external browser to see them. It would be great if this 64-bit configuration could be tested in a future release. I tried asking people in the help thread. I looked in the error log (Help->About Rssowl->Configuration details...) and didn't see any error messages. I don't know SWT.
afaik RSSOwl's internal browser does not support 64Bit flash yet.