A Listen Later playlist is like a podcast, which is distributed via RSS. You can subscribe to a Listen Later playlist via the RSS feed on any podcast apps.
On a Listen Later playlist page (Example), you can find the RSS feed by clicking on the SUBSCRIBE button:
Or you can simply click on the "Subscribe on podcast apps" button on your phone and directly choose a podcast app:
Known issues with podcast apps:
Apple Podcasts: Works perfectly.
Overcast: 1) There may be a few minutes to a couple hours delay to sync up your newly added episodes. 2) If you see "Not Found" error, just add "http://" to the RSS url.
Pocket Casts: You will get "Search failed" error if this is the first time you add your playlist to Pocket Casts. Try again then it will work.