the flash bridge is written in AS2 and is compatible with flash 8, so that the Flex Ajax Bridge is not available. You could use it, in which case you will avoid completely the flash bridge and use just the web client (the bridging will be done through your code using the Flex Ajax Bridge instead of using our bridge).
I really don't know if a rewriting of the bridge to use the Flex Ajax bridge will be done, we usually advice to use the native flex client that is not available with the Moderato edition.

Also what is that line for?
lsEngine.connection.setAdapterName("STOCKLISTDEMO" );
This line tells the client which adapter connect to on Lightstreamer server. Please check out the General Concept document available under the DOCS-SDKs folder in the distribution.