Hi there!
Great question!
If both forms are connected to one list and that one list is connected to a flow, a user will not enter a flow a second time if they have already filled out one form and gone through the flow previously. The reason is that users can only go through a List Triggered Flow once. Even if they use a different form to sign up, with the profile property attached to the form, Klaviyo will recognize that they are already in the attached Lists and have gone through the Flow once already. The only thing that would change for this profile is that it would now have the new profile property attached and its $source property would update to the second form.
I’d suggest checking out these similar Community topics that can help you gain more insight!
Finally, I’d recommend checking out our Klaviyo Academy courses to build on your Klaviyo knowledge if you haven’t already:
Thanks for participating in the Community!
-Taylor