Hello,
Thank you for reaching out and I am happy to answer.
There are no known compatibility issues with W3 Total Cache and Woocomerce/Flatsome theme.
The Pro version of the plugin unlocks additional features like eliminating render-blocking CSS, Image conversion limit, FSD CDN, etc.
I would recommend installing and configuring the community version first and getting the Pro if additional features are needed to improve the speed of your website, and of course, getting the Pro support.
Thanks!