not specificly the sony reader app, but you can download some other Epub Readers like moon+ reader, and sideload the Sony epub books over, its not quite as simple to sideload them as with other android devices but there are many here that do that kind of thing and searching closely you will find help on how do sideload (i have never tried it since all 800 of my books are kindle format) perhaps jessica lares here can help you, she seems to be a bit more knowledgeable about kindle fires than most i se on here
