my 6 1/2 year old lab swims almost daily (several times in the summer) in our chlorine pool. I haven't noticed any harm from the chlorine other than it seems to dry his coat out a bit, but we usually keep his coat shaved fairly short. he's always had flaky skin, so I try and give him a bath with extra conditioners for sensitive skin.
We have a salt water chlorine generator for our pool, so the actual chlorine levels at any given time are less than they might be for a regular chlorine pool. Having said that, Lily swims daily with far more benefits than negatives.
The chlorine helps keep her and the pool clean, but it does cause some drying. I make sure she gets plenty of yogurt and occasionally mix a little olive oil into her food and that helps some. She's still going to have a little dry skin, but nothing overwhelming that we've noticed so far.
A side benefit to the great (easy on the joints) exercise she gets from swimming, she loses some hair in the pool and its filtered out by the skimmers and the filters ... so less in the house.