Feed Tube uses youtube-dl to download a full playlist or channel into a directory. It can then generate a podcast RSS file which can be read by a podcatcher like Podcast Addict.
go get github.com/guywithnose/feedTube
youtube-dl with codecs necessary to encode to mp3.
Feed Tube works best with a publicly accessible server. If you control a server at podcast.awesomechannel.com running a webserver like Apache or Nginx with a doc root at /var/www, you could run this command:
feedTube channel 'AwesomeYoutubeChannel' \
--apiKey 'YOUR_YOUTUBE_API_KEY' \
--outputFolder '/var/www/podcasts/awesome' \
--baseURL 'https://podcast.awesomechannel.com/podcasts/awesome' \
--xmlFile '/var/www/podcasts/awesome.xml'
You could then add https://podcast.awesomechannel.com/podcasts/awesome.xml
to your podcatcher and you can listen to your favorite YouTube channel. You can even add that command to your crontab, and you'll automatically get new content as it is published.
For more information on getting a YouTube API key read this or watch this.