yes, have flown away is the "passe compose " and we can either say have flown away or flew away. THis would not be the case for the imparfait where se volaient could only be translated by flew away in English. We would not translate the imparfait as :have flown away" Therefore, have flown away should be correct.
Parce que cela se traduirait par: "Les oiseaux ont pris leur envol." See: https://www.lepopulaire.fr/limoges/vie-pratique-consommation/2017/10/02/les-oiseaux-malins-ont-pris-leur-envol-leur-atelier-collaboratif-a-ouvert-ses-portes-a-limoges_12572506.html