Visual Workflow – Toast Message Not Appearing When Triggered from Flow

You cannot create the visual flow at run time, meaning drop the flow only when your flowNotCompleted is true. To achieve this you can use $A.createComponent which will create another Aura component and be placed in init method. Lets call it as child component with name as 'flowCarrier.cmp'

Now we need a way to destroy the dynamically created aura component can use cmp.destroy(); method (check the last section of the same documentation link)

Documentation for dynamic component creation

So when a your flow completes, in the handleStatusChange's FINISHED status, you can pass an application event to the parent component to destroy the child component making the flow go away.

You cannot remove the opening of the model, it will be there. I would suggest to show messages in the quick action model instead of a toast using slds alert.

https://www.lightningdesignsystem.com/components/alert/

That way users can see multiple messages, they wouldn't need to close 2 things.