Despite having lived next to the North branch I never kayaked in it until this fall (2020).  An easy put in and take out spot is at Clark (Richard) Park at 3400 N Rockwell.  There are rentals available in season.  I am not sure if there is a bathroom at the facility.  You can launch kayaks or canoes from the docks and go in either direction.  The park is busy as there are baseball diamonds and a lot of other activities.   So arriving early on a weekend day is advisable. This is a wonderful urban journey going north or south.  The current does flow south but the current is not a concern.  There is always plenty of water year round and the river is wide.  You will see power boats as well as Kayaks and canoes.  The attached picture was taken on Nov 7th when we could kayak in t shirts!  Had to take advantage of that day.

Best Wishes to all for a great 2021

https://www.chicagoparkdistrict.com/parks-facilities/Clark-Richard-Playlot-Park/