There are two ways to know if you are looking at a new submission and one important thing to note.
Method 1: Each time a student submits a Noteflight assignment the score becomes a 100 so that the student can pass on to the next module. If you did not assign the student a 100 then each time you see the grade 100 you'll know that this is likely a new submission or at least one that you have not seen yet.
Method 2: In the SpeedGrader or the Gradebook the date for each submission is shown. If there are multiple submissions on multiple dates then you can see a menu listing of each date:
Also in the SpeedGrader you can go to the options menu (the gear) and select the option for viewing submissions by date they were submitted. This will put the latest submissions at the bottom of the list.
Lastly, the one thing to note is that the Noteflight score will always show the last saved version no matter which submission you are viewing. If you or your students would like to see past saved versions of a Noteflight score that can be done in Noteflight.
Let me know if this helps or if you have any further questions.