The question as phrased, the answer is no. It is not legal. If the 16 year old engages in any sexual conduct with the 13 year old, they could face statutory rape charges and the parental consent assuming there was any would have no bearing

Is a 14 year old dating a 16 year old illegal?

In general, it is not illegal in most states to date a 14 year old. Problems arise when the relationship turns sexual. Then there could be very serious criminal issues