So, easiest to reach from Prospect Heights and Park Slope is Dog Beach. To get there, start at what is called the Tennis House, off of the 9th St. entrance, and walk to the foot of the path leading downhill. It's just a tiny little cove in which to take a dip and play a wee bit of fetch, and there are lots of other dogs there too.
However, for real swimming, and plenty of room for full-on fetching, and without competition for space with other dogs - I really like bringing my pups a little further into the park, to Prospect Park Lake, which has a less dog-visited beach.