Is a travel agent agent allowed to book a flight for a Jew to fly on Shabbos, assuming that the person would be able to purchase the ticket on his own?
It is forbidden to sell a flight ticket to a Jew that will be flying directly on Shabbos, for both the reasons of “helping one do a sin” and “Chilul Hashem”.
Helping one do an Aveira – See Shulchan Aruch Admur Hazaken (Orach Chayim 347:3). See also Mishneh Lemelech (Hilchos Malveh Viloveh 4:2). Birkei Yosef (Choshen Mishpat 9:1 Ois Gimmel).
Chilul Hashem – see the Tosfos Yom Tov Yoma 8:8.