Can I move an email to a later date in a LIVE flow?

Oooo, this is a good question.  The Klaviyo help articles has a great walkthrough on what would happen:

Here’s a link to the article, but I’ll copy/paste the section in here as well:

Contacts are scheduled for all steps in a flow one-at-a-time, and they must move through one step before being scheduled for the next.

This means for those moving through a flow, any changes made to steps still ahead of them will impact their journey.

However, if someone is already scheduled (in Waiting) for a given step, they will remain scheduled for that step even if you move it elsewhere in the sequence. Additionally, say they are scheduled (in Waiting) for a first email or SMS, and you adjust the flow to add steps before this first touch, they will not receive these steps above unless you back-populate them.

For example, let's say you have a flow series with four emails:

• Becky received Emails #1 and #2, and is currently scheduled for Email #3. While Becky is still scheduled for Email #3, you drag this email to the top of the flow.
• New contacts entering the flow will get this email first, but Becky will still get it at her originally scheduled time.
• After Becky receives Email #3, we will attempt to schedule her for the next step (Email #1). If a contact has already moved through a step in a sequence and arrives at it again because you've reordered the steps, the contact will not be scheduled a second time. In this case, you placed Email #3 before Emails #1 and #2, but because Becky already received Emails #1 and #2 she won't be scheduled for them again.
• Becky will be scheduled to receive Email #4 because it is the next email in the sequence that she has not already received.
• The only way that Becky can receive any new emails added before the next email she is scheduled for, is to back-populate.