David,
A Linux version is on the feature request list, but not high priority.
As you probably discovered, the Toolkit right now comprises two pieces relative to your question: a Flash authoring environment and a local server (called the Hub) that handles the communications between the Flash widgets and devices connected to the Hub.
It would be relatively easy to port the Hub to Linux, and there is a Flash player for Linux. The problem is the Flash authoring environment is not available on Linux, so you would have to author on a Mac or PC and then move the resulting SWF file over to Linux.
.andy