Once you've imported your podcast to Omny Studio, you can easily migrate to Omny Studio without losing your existing subscribers. All you need to do is tell iTunes and the other podcast directories and apps to pull from your new RSS feeds. This is done by applying a re-direct from your old feed to your new feed.
If you've uploaded episodes to your old host since your initial import to Omny Studio, please follow this guide to re-sync your feed with Omny before applying a re-direct.
To move from your own self-hosted RSS feed
You will need to set up a 301 permanent redirect from your old RSS XML URL to the new Omny Studio RSS feed URL.
Setting up a 301 redirect will differ depending on your server or content management system, so contact your host or website administrator if require assistance.
Note: Although iTunes will normally pick up on changes within a few days, you should leave the old feed in place for a few weeks to ensure all subscribers are moved across.