Sounds in the ballpark. You just want to have your breathing *entirely* under control before starting the next repetition. This is pure neuromuscular stuff and you don't want the lactic-acid mechanism to be engaged...which it eventually would be, recoveries were incomplete.
Different things work for different people. Some might find that, after their gradual deceleration from the flying 30, a slow walk back to where they started is sufficient; others may find that, if they did the flying 30 on a track straightaway, a walk around the rest of the track and back to the starting point (~300m?) works better. And still others might find that simply standing for (most of) their recovery works best for them. You can experiment and decide what seems to fit your situation.
Whatever you decide about your recovery, a couple of tips:
1) Always do flying sprints with the wind (if there is any) at your back, helping you along.
2) Always get a thorough warmup before the first sprint, of course; and on cooler days, be conscious of not taking *so* much time between reps that you start to get chilled.
3) It varies from person to person, but most seem to benefit more from flying sprints if they focus more on increased stride *rate* (= turnover) rather than increased stride *length*.
Anyway, have fun! It feels great to just fly along, doesn't it?