Red Prince has two locations I am aware of to find him at. If you have not left Fort Joy into the Hollow Marshes, Red Prince can be found on the rock not far from where you was up on the beach. If you have unlocked Amadia's Sanctuary and transported the Red Prince to the sanctuary, if you dismiss him, the Red Prince should be on a platform near Exter.
From the image, your characters are currently right where the Red Prince should be. I suspect you haven't had Red Prince in your party since entering the Hallow Marshes, so he "should" be back at the rock. If you have transport the Red Prince to the sanctuary, it may be that he is just on a time delay to show up at his location in the sanctuary. As such, just burn some time in game doing something else and check back later.
The only other locations it would make sense for him to be at would be at either of the dreamers.