I know that out of desperation Moshe asks God to kill him and I don't necessarily see any reason it would be forbidden but I was curious if there was any discussion, halachic or otherwise, as to whether or not someone may request that God kill him.
This definitely isn't a halakhic answer, but there is a remarkable story about the Klausenberger Rebbe: when he was in Auschwitz and Muldorf he prayed for death, and then after the war he did teshuvah.
Variants of this story appear on the Yad Vashem website and in the biography "Lapid ha-Aish", written by Aharon Surasky and translated into English by Judah Lifschitz as "The Klausenberger Rebbe".
Choni HaMagel does exactly that in Taanis 23a. Since he was one of the gedolei hador I would assume it is ok
While not a direct halachic source, we often learn halachot from the behavior of righteous people in Tanach; several, including prophets such as Yona (4:3)and Eliyahua (1 Melachim 19:4), as well as Iyov (6:9, passim) asked God to kill them. I am not aware of this being viewed as a sin by any of the commentaries or chazal (I understand that absence of evidence is not evidence of absence, but it does make a strong case).