While what Kim suggests sounds like it will work, mentioning in the text is the key. Setting the smart campaign to go through flow only once doesn't actually prohibit them from submitting more than one entry. It doesn't send the follow up e-mails and doesn't add multiple entries to the list, but without strong language in the text, the recipient has no way to know their second entry wasn't counted.
Is there a way that if the form has already been submitted with that e-mail address it can be set to reject subsequent submissions?