Shared hosting, Coldfusion 8 & Livecycle Data Services ES

The LCDS that comes with CF 8 is LCDS Express which is licensed for single CPU single application. Since shard hosting is multiple applications, LCDS is not licensed for that and won't be available on a normal CF shared hosting account.

Look into using CF 9 with the AIR integration features. Doesn't use LCDS but BlazeDS so the licensing is not a prolem, and with the syncManager.swc library you get you can do the whole data synchronization.

It really depends on the hosting provider.  The ColdFusion 8 install (Standard & Enterprise) have the ability to install a LCDS "trial" which after 30 days will revert to LCDS ES which is free, as long as the server that it's installed on has no more than 1 processor (up to 2 cores though I believe).

To more specifically answer your question, it really depends on whether the individual hosting provider has installed and offers this option to their clients.  The use of LCDS with Flex required configuration of a data-management-config.xml file and certain ports may need to be opened up for rtmp vs. polling transfer methods.  I'm not sure exactly how this would work given a shared hosting environment and if you could sandbox the configurations per client.

The sure way to get this setup (and the method I've used for the past few years) is to get yourself a dedicated box (which can be had for less than 100 dollars, especially given the processor limitation on the LCDS licensing) and get yourself a license for CF8 while they're still available.  CF9 will still support LCDS integration, but the install isn't seamless like it is with CF8.  During the install process for CF8 you can choose to install LCDS and after a bit of configuration you're all set.