Easiest way is to email the song files to yourself, open the email on your phone, tap on the song file attachment, and there should be some form of destination dialog that has the Walkout Songs app listed to copy to. Then the Walkout Song app will ask you if it is a song or player announcement and store it in an import folder where you can browse songs for your players.
You can also transfer songs using cloud storage like dropbox, google drive, and such. Put the song on the cloud service, open the cloud service app, find the song, tap on it and the option to open with Walkout Songs should be there.