As bigcatdiary has already pointed out the reason he wasn't allowed to double up is in rule 17.4.1.
No Elite League Club can have more than 2 doubling up riders, and as Kerr, and Rose are already doubling up, that rules any other Kings Lynn riders from doing so. (although there is also the issue regarding the assessed average.)
As Danny King pointed out in his interview in this weeks Speedway Star, his average was low enough to double up, but he was unable to as Ben Barker, and Edward Kennett were using up Birmingham's quota. (Until Kennett was replaced)