Question: I plan to fly from New York during the night of Purim (after Megilla reading) and arrive in Jerusalem in the afternoon. Would I have to hear Megillat Esther in Yerushalayim before the end of the 14th of Adar, or is it enough that I will hear it there on the 15th?

Answer: If one is, at day break of the 14th of Adar, in a place which celebrates Purim then, he is obligated to hear both the day and night Megilla reading on that day (Megilla 19a). This is so even for a resident of Yerushalayim (sometimes intention makes a difference, but not in this case). This is learned from a pasuk (Esther 9:19) that discusses people who "are sitting in an un-walled city" in addition to residents of such cities. The same is true if he is in an uninhabited area (including a plane over the ocean), as the 14th is Purim for anywhere that did not have a wall at the time of Yehoshua (Rama, Orach Chayim 688:5). If he is subsequently in Yerushalayim on the 15th, he is obligated to hear the Megilla on the 15th as well (Yerushalmi, Megilla 2:3).
Not all agree with the apparent ruling of the Yerushalmi that one can be obligated to hear the Megilla for two days. The way the Korban Netanel understands the Rosh, the Bavli argues with the Yerushalmi and says that the place where one is at daybreak of the 14th sets his status and determines on which one day he will be obligated to read or hear. Therefore, Rav Ovadia Yosef says that one who starts Purim outside Yerushalayim and returns by daybreak of the 15th reads with a beracha on the 14th and without a beracha on the 15th (see Yalkut Yosef, Moadim, p. 306). Rav Frank (Mikraei Kodesh, Purim 19) goes further, saying that even the Yerushalmi required hearing the Megilla on the 15th after hearing on the 14th only if one moved permanently from one place to the other in between the respective reading times. However, we have not found any opinion that exempts one who is outside Yerushalayim on the morning of the 14th from hearing the Megilla on that day due to plans to hear the reading in Yerushalayim on the 15th.
The plan to arrange to hear the Megilla when you get to Yerushalayim toward the end of the 14th raises a few halachic issues. One is that only someone who is obligated in reading on the 14th can read for you. This is based on the Yerushalmi (ibid.), which says that one who celebrates Purim on the 14th cannot read the Megilla on the 15th for those keeping the 15th because he is considered like one who is not obligated in the mitzva. Rav Frank (Mikraei Kodesh, Pesach II:66) minority opinion is that the Bavli disagrees with this Yerushalmi, with the logic that the general obligation to read the Megilla along with the concept of responsibility for a fellow Jew’s religious obligations suffices to be considered obligated. While there is some basis to claim that regarding the 14th, all are considered obligated (see Yabia Omer, OC I:43.17), the consensus is that the ba’al korei for the 14th should be one who is obligated that day(see Yalkut Yosef ibid.). (His having fulfilled the mitzva earlier is not a problem.)
Eating is also an issue. It is forbidden to eat a meal before fulfilling the obligation to hear the Megilla (Shulchan Aruch, Orach Chayim 692:4), both at night and during the day (Mishna Berura 692:15). While one is allowed to snack, some say this is only in the case of significant need (ibid. 692:14) and while snacking sometimes means anything less than a k’beitza of bread (ibid.), some say that one should not eat more than a k’beitza of anything (Mikraei Kodesh (Harari) Purim 4:6 in the name of Rav M. Eliyahu). Certainly you would not be allowed to have the Purim Seuda, which you will need, until after Megilla reading. (For mishloach manot and matanot la’evyonim, appointing an agent in advance is likely a wise step – see Living the Halachic Process, vol. I, D-13 regarding some timing issues.)
Due to these complications, most people would probably avoid a trip such as the one you are planning or at least try to arrange to read or hear a valid reading from a kosher Megilla on the plane.