I can say that I personally use the Android Engine Driver app on my Kindle with JMRI on my home WIFI. It works great. Like others say, you need JMRI running the WI Throttle Server on a computer connected to a wireless network. It takes some time to set up but has run flawlessly for me.
What they said above. However, the place to start is with JMRI. Your DCC system needs to have a serial or USB connection port. Then you need to be able to connect your layout to your computer, and JMRI does that.
http://jmri.sourceforge.net/
Elmer.
The above is my opinion, from an active and experienced Model Railroader in N scale and HO since 1961.
(Modeling Freelance, Eastern US, HO scale, in 1962, with NCE DCC for locomotive control and a stand alone LocoNet for block detection and signals.) http://waynes-trains.com/ at home, and N scale at the Club.
There is an app for ipads/iphones, etc (WiThrottle) and a similar one (Engine Driver) for Android devices that both work with JMRI. Of course, you also need a control system on your layout that JMRI can talk to.
Since the Kindle runs a heavily-customized version of Android, it may be possible to use Engine Driver on those devices. I guess it depends on just how much customization (read: locking down) Amazon has done to it.
I don't know about the Kindle, but there are apps for smart phones to do this. You need a WIFI signal,JMRI and a computer interface for it to work. Joe
I heard a rumor that one can operate model trains with a particular app for kindle style readers. Can anyone shed some light in this for me? Thank you.
Old fat Robert