You can't publish a Flow as a Template that uses custom APIs.
Basically I have a series of flows I want to make with minor modifcations. I want the ability to copy an existing flow and modify it without being forced to publish it as a template, espeically since in this case I can't since it uses custom APIs
I, too, would love this feature. I'm sure I'm not the only one with some pretty complex (and long) flows. I need these flows (with a few tweeks) for multiple business processes. Having the ability to "duplicate" a flow will drasticcally reduce the time it takes to create these workflows.
You can read more about this feature here: https://flow.microsoft.com/en-us/blog/make-a-copy/