Hi @amarin27 - welcome to the community!
Unfortunately, by definition, any Flows triggered by a List Subscription can only go through the Flow exactly once. You can see here in Klaviyo’s documentation:
Contacts can only receive a list-triggered flow once. If someone is removed from a list and then re-added to that same list, they will not re-trigger the flow. For example, if someone unsubscribes from your newsletter list and then re-subscribes, they will not receive the welcome series again.
What I recommend is adding a hidden field and value to this new form like “sales-signup” with a value like “1” or “true.” Then, create a Segment where Property of the User → sales-signup = 1. Then create a new Flow that is Triggered on that Segment.
In this way, new subscribers will go into your Main List and have that Custom Property. Returning subscribers (who subscribe again) will have that new Custom Property. Both will go into the Segment Triggered Flow to receive the first Flow email specifically for your Sale.
Also remember, you may want to also put in Message Filter or a Branch Condition or a Time Delay if you don’t want net-new subscribers from getting the Welcome Flow First Email and the Sales Flow First Email at the same time (unless you want them to!).