Symphonic does not currently offer podcast distribution as this requires a slightly different distribution process than music distribution. If Symphonic officially begins support for this type of distribution we will be sure to notify all our clients.
Spotify Podcast Application
You can in the meantime submit a request to Spotify directly to host podcasts which they will review and possibly approve, you can apply here. Any questions can be referred to firstname.lastname@example.org.
SoundCloud is another popular location for podcasters looking to get started. Information on getting started in podcasting on SoundCloud can be found here.