Fortunately, University of Leicester students have been putting a lot of study and thought into this very question. Two scientific papers Gillyweed - Drowning With Gills? and Revealing the Magic of Skele-Grow analyze two of the many magical items that appear in the Harry Potter series. Gillweed, you probably know, is the plant that Harry consumes allows him to grow gills and webbed hands and feet during one of the tasks during the Triwizard Tournament.
This process was carefully examined by natural science students, Rowan Reynolds and Chris Ringrose. They determined that, based on the size of Harry's gills and the maximum oxygen use of a boy Harry's age, he would need to process 443 litres of water at 100% efficiency per minute for every minute that he's under water. This means that the water would need to flow at 2.46 metres per second.
In their conclusion, they found that Harry's gills probably wouldn't be able to function properly. However, had Harry opened his mouth during swimming, his gills would be more feasible.
As you may remember, Skele-Grow was a potion that was used to heal Harry's arm when his boned had been removed in Harry Potter and the Chamber of Secrets. Students Ringrose, Leah Ashley, and Robbie Roe concluded that the Skele-Grow allowed Harry's bones to heal at about 90 times the normal rate. Their calculations show that the bones regrew using energy amounts of "at least 113, 050kcal, giving a power output of 6, 443W." This means that this potion must have unexplained magical properties to be able to heal bones that quickly.
Although we Potterheads can dream, it seems as if these two items are only possible in the Wizarding World.
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