As long as the proper BITSTREAM is being loaded, you just copy the ELF into your file system. If you are using a flash filesystem, just copy the file to the SDCARD rootfs. If not, you will need to inject the application into the image.ub, so it is present after boot and ramfs creation.
As a test, you can just copy the application to a standard thumbdrive and assuming you have the linux permissions proper, just execute from the thumbdrive. Again, this is assuming you have the proper bitstream loaded.
If you take a look at SDSoC, it actually handles ALL of this for you, based on the BSP settings.