As a preface, I think the question might benefit from some further clarification. Aside from considering the matter in the light of Scripture, it seems many would likely agree that there is a significant difference between what might be called "responsible gun ownership" and the subculture often highlighted by the media that defiantly and aggressively glorifies gun ownership.
I'm aware of no Scriptural basis on which gun ownership can be advocated. In fact, the first verse that comes to mind is Mt 26:52:
Then Jesus said to him, "Put your sword back into its place. For all who take the sword will perish by the sword."
No historical doctrines come to mind, either. Roman Catholic "Just War" doctrine doesn't seem related to the issue, though someone with better knowledge of the Church of Rome may know otherwise.
The strongest potential connection I can see between the church and the "gun culture" would stem from the independent, uncompromising, perhaps "defiant" character of the Protestant Reformation in relation to the Church of Rome in the 16th century. (Some of Luther's "antics" come to mind). Elements of the same uncompromising approach can be seen in the choice of the Puritans to separate from the Church of England.
But, while I'm not a pacifist, I don't mean to suggest that the Bible encourages gun ownership. As far as I'm aware, it does not.