Here's your answer. (I was an electrician before I became a professor and lost my hair and my mind):
The dictionary definition is correct. Zero. It's commonly used to describe wire sizes as well as buckshot. We say "aught," but we actually mean 0 size wire or buckshot. This is commonly used and accepted slang.
However, in the case of the 30.06, it refers to the year (1906) that the M1903 Springfield rifles were chambered to accept a new cartridge. So, in this case, you have a thirty caliber bullet 30, and the year it was first used on the Springfields ('06)...so in this case, "thirty aught six" is incorrect slang. It's "thirty oh six," referring to the .30 caliber and 1906 year of introduction.
It's a case of "everybody says it," but it's still wrong.
Hope that helps
MP