I haven't taken the flixbus to Rome from Naples but last October I took it from Salerno, stop in Naples then to Bari. I used the app to book on my phone. I booked the ticket 2 days before leaving. Using the app is very straight forward. I just checked now and I could still book tickets for tomorrow, Naples to FCO, both the 10am and 1:10 departures are still available. So, you might want to download the app now, and check periodically to see if they book up or how much the price changes.
The bus depot is behind the Naples train station. If you're walking there give yourself a few extra minutes, it's really big and not intuitively obvious how to get there.
FYI we booked 'first class' which just meant we got to pick seats in the first few rows. We took seats 3c and 3d. The seats are a little tight but fairly comfortable. My husband felt cramped because the person in front of him sat back and the seat reclined into my husband. He asked the guy to adjust and he did but that poor guy decided to sit forward the whole trip because he couldn't get his seat to lock upright. If you choose regular seating they're not assigned you just walk back and grab a seat. I'm not sure it was worth the few dollars more to get specified seats but it wasn't a very expensive upgrade.