To prevent someone who has subscribed and purchased just add the following flow filter and have them go to the same list you are using for your embed form:
 

Hey @JOWPM 

Welcome to the community and congrats on your first post! Happy to help with your popup signup form.

Within the Behaviors & Targeting section of the signup form, you can set it to NOT show to customers who are already in a list or segment within your accout and therefor will not receive the discount code. 

Hope this helps!

Hi @JOWPM Great answers above, but also wanted to add - when you are editing your form, on the button, make sure you choose the correct list from the drop down (whichever list you want your subs to enter). 

Thank you for your valuable responses!

How I can ensure they receive the desired flow? Is it possible to send two separate flows—one for the welcome series and another for the pop-up?

@JOWPM You can absolutely send to separate flows - create 2 lists - one for the pop up and one for embedded form. The flows will be triggered by joining that list, so you can create 2 completely separate flows if you’d like.

Katheirne