One of my limiters for the swim is shoulder mobility. I played tennis competitively as a kid and even then it affected me by checking my serve velocity as well as ability to get a good spin. Anyway, that’s neither here nor there… I just want to get faster in the water now. Anyone have a good routine to improve flexibility?
Yes actually. Look up Kelly Starett. I’m in Oz, but my physio here advises me to follow Kelly’s videos on shoulder mobility as I have poor internal shoulder rotation which means I have a weak catch in the swim but also lots of everyday cramping and tension. Seems to be improving since doing the stick in the shoulder method.
I’ve improved my shoulder mobility considerably with some simple exercises.
- Downward facing dog yoga pose
- Holding arms above my head, as far back as I can
- Grabing my hands behind my back, 1 arm above my head, 1 arm behind my back.
I did a routine every night before going to bed. I would alternate between all three for 3-5 sets, holding each pose for up to 1 minute. I think #3 was the most useful for me, but all three were good. The first few sets were tough, but by the end I could feel myself getting more flexible and the poses got easier. In the beginning I used a towel or a stick to increase my reach, but now I don’t need it anymore.
It takes time, so be patient. Also, swimming a lot helps! 
I don’t have a “routine” per se but rather many, many swimmers stretch their shoulders 10 times or more every day, just because they get tight after any period of sitting/driving, etc, and stretching them out just feels really good:) I am all the time stretching 1 or both arms over my head. You can even do this in the car while driving, use one arm to steer and stretch the other arm back over the seat and push against the roof of the car. The very best stretch, at least IMO, is standing up leaning against a wall or doorway, and stretching your arms over head in the streamline position. Swimmers just stretch a lot because it feels good:)