When Ennis phones Lureen in order to know what has happenned to Jack,she says when talking about BBM:-
Well, he said it was his favorite place. I thought he meant to get drunk. He drank a lot. And yes,it's sure that he drunk,I don't know if until the extreme of being drunk; they say that people drink in order to "forget"...Did,then Jack drink to forget the reality of his life?.What's more: Did he drink enough as to destroy little by little his health and,therefore,his own life?.
I'd said more;somebody has told that he was so opened in his sexual tendencies that even he took some dangers; the dangers Ennis wanted to avoid being more protective and also closer in himself than Jack.Maybe he arrived to a point in his life when he,simply,didn't mind if somebody could discover his tendencies or not...and the consequences this could have for him?.
Jack was a person who was always looking for love and never found it completely:neither at home,when his mother's love and affection wasn't enough to hide the pain that a sever father could cause in a young mind; nor at his own home,with a cold wife who showed him as one more of her prizes and company profits; even nor with an Ennis who was spending all his time-their time-running away from this "sweet life"and,more than often,from Jack himself.Maybe the reason of his taking risks wasn't that he was open enough as not to worry if people knew it or not; maybe the reason was being too tired of living that way and,therefore,a unconscious wish of ending.Had Jack,then,some self-destructive tendencies?.
Interesting questions. I just found this topic and joining late. My response is that Jack was not self-destructive deliberately. He had no intention to destroy the life, as pitiful as it was, with Lureen and with Ennis. He may have said, "I wish I knew how to quit you." But he could never quit Ennis. The life with Lureen was destroyed that moment when old man Newsom threw 'em keys at rodeo and put him down, and all 'em other times. No man was good enough for his little girl. When Jack stood up to the old man that Thanksgiving, Lureen smiled and was happy.
Jack drank a lot because even with the good life he had in Texas, his life was empty without meaning without Ennis. He drank to forget the sweet life he could have, the sweet life he had every few times each year when he drove 'em fourteen hours each way to be with the love of his life. He wouldn't do anything to jeopardize that. He want that sweet life too much.
We really don't know much more about the "risks" he took in Mexico or with Randall. The gas station scene was deleted, in part I believe, because Ang Lee wanted to stay true to the words in the short story. It is one thing to put flesh on the bones of the raw words in the short story. It is another to change the height and dimensions of the characters. Jack may or may not have been taking more risks with Randall. He may or may not have been murdered.
One thing was true, about Jack wanting to bring Randall up to Lightning Flat. We don't know much more about that relationship, but it is no more self-destructive than going to Mexico. It was what men with pent-up desires and no place to go would do. In 'em old days, back before Stonewall and liberation, there were not many places for gay men to meet. It was risky no matter what Jack did, if he wanted to live life true to his feelings. He preferred to take the risk living the sweet life with Ennis, but when it got real bad, since he ain't like Ennis, he would go and do whatever it takes. Drinking a lot was the usual way.
It maybe even true, that at the end, after the final confrontation, in despair and pain and even hopelessness, Jack finally accepted the futility of waiting for Ennis to share the sweet life (hence the comment to his Pa about Randall) and got subconsciously sloppy with his car, or with hiding his tracks, or whatever. Perhaps that is why he was okay driving all 'em distances all 'em years and never a problem, then ending his life on a lonely dirt road while changing a flat.

So, no, I don't think Jack had any self-destructive tendencies, until perhaps the final moments in his life, if he wasn't murdered. If he
was murdered, then I may go further and say that he never was self-destructive...he loved life, and Ennis, too much to quit it and him.