Answer: The Mishna (Taanis 26b) writes that from when the month of Av begins until after Tisha B’av, we reduce in our enjoyment. The Shulchan Aruch (OC 551:2) lists a few restrictions that must be observed during these nine days. The Noda Biyehuda (OC 2:105), however, writes that one should also avoid other activities that one enjoys during this time. Thus. R’ Shmuel Wosner (Shevet Halevi 10:26) and R’ Ephraim Greenblatt (Rivevos Ephraim 1:374) write that one should avoid going on outings during the nine days.
The Shulchan Aruch (OC 551:18) writes that one should also avoid doing anything potentially dangerous during the three weeks. Following this, R’ Shlomo Zalman Auerbach (Halichos Shlomo, Bein Hametzarim 14:24) writes that one should avoid flying during the nine days. While flying is considered a safe means of transport, one still says the beracha of hagomel afterwards due to its potential dangers.
Nonetheless, R’ Auerbach allowed yeshiva bachurim learning in Eretz Yisrael to return home during the nine days rather than leave yeshiva earlier. Likewise, he maintained that it is permitted to fly to Eretz Yisrael during the nine days, and if necessary, even on Tisha B’av (afternoon).
In conclusion, while one should avoid flying during the nine days, one may travel to Eretz Yisrael then.