Congrats,
I am on my second drone from DJI, now a Phantom 4. They are amazing! I haven't synched a lights show to a video..... yet only because I haven't had an animated light show to video but that will change this year. This is my first year with the blinky lights. But on past experience with Drone cinematography I have had great success with AVS4You in syncing up other videos with sound and it wasn't difficult to get thinks to sync up. AVS4you has some other great tools as well and I don't know what it costs now, but it was well worth what I paid for it. I have taken several videos and synched it to a recording that was made on the ground at the same time and it was pretty simple. Another thing you might want to look at is a program called Litchi (https://flylitchi.com/) If you want a nice smooth video, this program is the way to go. You set up a mission in a web browser where you design every aspect about the flight and then you just start the mission with the push of a button and the entire flight is conducted without you doing a thing and everything is smooth. Here is a video that I made with Litchi a while ago https://www.youtube.com/watch?v=i9SsKZmRkJ4
Good luck and let me know if you have any other questions.