The Spotify app will only play files streamed or downloaded via the app. It will not show local files that you may have on your device.
The only way to get these into Spotify would be to transfer them to a PC and then sync to your phone as per the support topic here about setting up local file sync: Listen to local files
Make sure that you are on the same WiFi network and Windows & third party firewalls are configured to allow the Spotify connection through.
Another point to note is that sometimes if a track is stored locally & is also available to stream then when you sync to your device it will automatically use the Spotify streaming version but the data from your playlist. If for some reason the metadata such as track length differs this can cause conflict and break the track. In this instance you are best off removing the local file from your playlist on the desktop and adding the track from the Spotify server then re-sync. This should fix this issue.
Please use the search feature before posting a problem/bug/idea. What's a Spotify Rock Star, and how do I become one? Using Spotify Since March 10th 2009 Twitter: @mechanimal82