This is a perfectly correct and natural sentence. The rough meaning is "if somebody encourages Burkle to talk about his latest business scheme, he will talk for a long time." - - - - - "Get" and "have" can be used as causatives. Ex: I got/had my fence painted. I am getting/having my fence painted. I will get/have my fence painted. Source: English Grammar in Use by Murphy, 5th ed, unit 46C. [excerpt] When are you going to get the roof repaired? I think you should get your hair cut really short. [end excerpt] - - - - - "Go" can be a synonym for "talk" or "say." Ex: And then my brother goes/says that he is looking for a better job. Source: Collins online dictionary - go / other uses number 7 Ex: He goes to me: 'Oh, what do you want?' - - - - - - The original sentence is an implied type 0 conditional. But [if/whenever you] get Burkle going ..., [then] he can't keep quiet.

The verb "get" is highly flexible, having hundreds of possible meanings. For that reason, it is a "sloppy" verb that is used so much only because it allows a person to speak English without thinking or choosing words carefully. It means almost whatever a speaker wants it to mean, so long as it is loosely connected to the idea of "acquisition". The meaning of "get" is determined largely by context. Usually, it is obvious what a speaker wants it to mean. In your example, "get Burkle going about..." probably means one of these things: "allow (or 'permit') Burkle to start talking about..." "encourage Burkle to start talking about..." Since "get" is used so often, it is important to study examples like this one. However, while learning English it is generally not a good idea to use it yourself. The sloppy verb "get" has a tendency to displace good verbs, lowering the quality of your speech. Use "get" only in common expressions like "they get along well", but avoid using it as a main verb in your sentences. Avoiding "get" will help you to learn good verbs and expand your vocabulary.

It means if you ask him about his latest business scheme he will talk about it a lot. Maybe he doesn’t usually say much. “To get someone going” here means to encourage someone to talk. It’s similar to “Don’t get me started on … (normally a subject you don’t like)