Your sentence is almost perfect! Here's a little correction to make it clearer:
Original: When geese swim, their feathers don’t get wet. All thanks to a special oil coating.
Corrected: When geese swim, their feathers don’t get wet, all thanks to a special oil coating.
Explanation: Instead of making the second phrase a separate sentence, combining it with the first makes it flow better. You can use a comma between "wet" and "all".