Are you using a Wait flow action before each Send Email flow action to set the date? If so, my guess would be that new additions to the smart list would flow through the first Wait step since it has already occured, but they would be sent the first email as well. You may have to add a Constraint to the first Send Email flow action to check that the date is on or before the date that email should be sent (screen shot below). You will need to add a form field to hold this date for comparison to the current system date.
If a new lead is added to the a flow it will start from the begining of that flow. The smart list itself isn't being processed it is the leads wtihin the smart list.
The new leads will get the first email in the sequence, proceed to the wait step and then recieve the second email 2 weeks later.
Jem | Debenu
If you add someone during a wait step, then it will wait until the completion of that wait step then start at the first flow step while the others carry on in the flow?