Chris at Thesis was quick to reply:
Basically, a .flv plugin needs at least one file in order to work, and that's a swfobject.js file in the document <head> (I've heard reports that these plugins don't work if the JS is embedded just before the end of the HTML document, which is generally where you want to place JS).
With the plugin active, check out the content of the document <head> while using the default WordPress theme. Then for comparison's sake, activate Thesis, and see if the plugin is serving the necessary files in the <head>. If it's NOT, then you know what the problem is.
Quite frankly, I don't see any good reason (from a coding standpoint, at least) why the plugin would work with 1.6 and then not with 1.7, but then again, plugin developers do some interesting things to initialize their code. The presence of the wp_head action call in Thesis 1.7 is enough to allow the plugin to initialize itself in the preferred manner, so as far as I'm concerned, there's no reason why it shouldn't work.
If you do discover that the Hana FLV plugin is not being initialized properly with Thesis 1.7, you can either dig through the plugin yourself and try to get it to initialize on the wp_head action hook, or else you can contact the plugin developer and suggest that he/she initialize the plugin with this standardized action hook (wp_head).
Finally, some developers test for the presence of the wp_head action hook in the theme's header.php file before initializing their code, and this is both archaic and unnecessary. If the Hana FLV developer has gone this route, then it's time for he/she to remove that archaic check, as the wp_head action hook does not, as a rule, have to exist in that file in order to function.