Can I gank from the left battlefield to the right battlefield if there are three battlefields, skipping the middle?

Yes, you can.

According to Rule 810.1.b, Ganking allows a unit to move from "a battlefield to another battlefield." There is no requirement in the rules that the movement must be to an adjacent battlefield or that you cannot skip over others.

As long as you control the units and the destination battlefield (and assuming the destination is not restricted by other game rules, such as having units from two other players present, per Rule 443.2), you may move your units from any battlefield you control to any other battlefield you control.