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REST API Equivalent: You can use the /config/{app}/flows/{flow}/copy operation to copy a flow.

To copy a flow from the Registration Flows page, complete the following procedure:

On the Registration Flows page, click the Actions icon next to the flow you want to copy and then click Copy:
In the Create a copy of dialog box, enter a name for your new flow:

Note that flow names must be unique within an application: if you already have a flow named MyFlow then you can't name the new flow MyFlow. On top of that, flow names can only contain letters and numbers, with one exception: the underscore character (_). As noted elsewhere, you can’t include spaces, dashes, commas, or other special characters in your flow names.
Click Save.

Keep in mind that, from the Registration Flows page, you can only copy the latest version of a flow. If you want to copy a previous version of a flow, click the Actions icon next to the flow name, click Edit, and then, on the Edit page, click Show Version History.

Copy a flow from the Registration Flows page

As noted previously, you can copy the current version of a flow from the Registration Flows page: all you have to do is click the Actions icon next to the flow you want to copy and then click Copy. That works fine, albeit with one stipulation: from that page you can only copy the latest version of a flow. If you want to copy an earlier version of a flow, you’ll have to access the version history and then copy the flow from there.

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However, after you reach the version history the copy process is the same: you use the same approach to copy a flow from the Registration Flows page that you use to copy a flow from the Edit page.

To copy a flow from the Edit page, complete the following procedure:

Click the Copy flow icon next to the flow you want to copy:
In the Create a copy of dialog box, enter a name for your new flow:

Note that flow names must be unique within an application: if you already have a flow named gms_flow then you can't name your new flow gms_flow:

On top of that, flow names can only contain letters and numbers, with one exception: the underscore character (_). But that's it: you can't include spaces, dashes, commas, or other special characters in a flow name. gms_flow is a valid flow name; gms flow and gms-flow are not valid flow names. If you type an invalid character (such as a blank space) the Save button becomes unavailable and you will not be able to save the flow until that character has been deleted. For example:
After entering the name click Save to create the new flow.

A note about renaming flows

To be honest, there isn’t a way to rename a flow. Obviously, you can copy Flow_A and then save it under the name Flow_B. However, this isn’t really renaming a flow, and for two reasons. First, when you rename an object you typically end up with the same number of objects as you started with: one. For example, suppose you have one file: File_A. If you rename the file, you’ll still only have one file: File_B. However, when you copy a flow and give it a new name, you’ll end up with two flows: Flow_A and Flow_B. If you no longer want a flow named Flow_A then you’ll have to delete that flow.

But, before you do that, keep this in mind. When you copy a flow the flow itself gets copied: the copied flow will contain the same data – fields, strings, screens, translations, etc. – as the original flow. What it won’t contain is the original flow’s metadata. For example, suppose Flow_A has 37 prior versions. When you copy the flow, Flow_ B will have no prior versions: that’s because the flow history is not copied over. (Which makes sense, seeing as how copying a flow means creating a new flow, one that has no prior history.) Whether that’s a problem or not is something you’ll have to decide for yourself.