I've noticed the rules talking about logistic rolls for vehicles but I cannot find a base availability for them. Have I missed something, or is it a scenario specific thing?

Generally speaking, you don't roll to get hold of a vehicle - you either get assigned one or you don't.

Where did you read about rolling logistics for them?

It was mentioned on page 387of the rulebook, in the introductory adventure section Dark Hunters. Second sentence states "It is best used if the Squad chooses to exit their transport for some reason - or if they lost the Chimera due to a poor Logistic roll at the start of the mission."

That would be in referance to the chimera transport being assigned as part of the Mission assignment gear on the previous page. You roll a logistics check to see what happened to the gear reserved for the mission Page 166 and this could result in none of it showing up.