Thank you for using Apple Support Communities. It seems like you want to use the Podcast app but you cannot find it on the iPhone. One reason you may not be able to find it if it is suggesting it is already is installed may be because it is restricted. I would recommend you read this article and use it to help troubleshoot the issue.
When you have Restrictions on, you might not see certain apps, features, or services. If you're missing an app or feature, or can't use a certain service, try turning Restrictions off. Also, make sure to check that you haven't removed certain built-in apps.
Use Restrictions on your iPhone, iPad, and iPod touch
Take care.