How about a set of wings with winglets on the end to reduce drag. For water use, the wings fold around the operator and create an elongated, streamlined shape, and the winglets from each wing lock together and form a propeller for underwater use. The inside of the leading edge of the wings contain the shafts that drive the propeller.
To transition to water, you just fold the wings back like a pelican diving for fish, or you just glide and land on the surface, then reconfigure for water.
Transitioning back from water to air is more difficult. Somehow, you have to get out of the water and get up to flying speed. How about the root of the wings reconfiguring themselves into a hydrofoil, which also lowers the propeller so it stays in the water while the contraption is skimming along on its foils. Think of an inverted gull wing shape, like a Corsair WWII fighter, except at this point the wings are still connected at the tips, to form the propeller. So more of a diamond shape, yet bent to form hydrofoils. You then go to the surface, reconfigue, and get up to speed on the hydrofoils. This configuration gives you enough lift to get into ground effect, then you can separate the wings at the back, stretch them out, and fly away. Or, if you don't need to fly you can just stay in hydrofoil mode and travel that way.
The big problem will be energy. It takes a lot of energy to fly under power, and to move at high speeds underwater. Moving slowly under water can be done almost for free, by inflating and collapsing bladders that allow you to dive and rise repeatedly, traveling directionally while doing so. So one answer to the energy problem could be that flying time is strictly limited, and all serious distance traveling is done by water with the wings used basically to get to and from the water. Or, if batteries are used, the wings could be covered in solar cells and the creatures travel in hops - landing on the water long enough to recharge batteries just enough to get them to an altitude where they can glide a few miles. Then they land and repeat.