Lifting by itself may increase your flexibility.
The authors debunk the myth that lifting can make you “muscle-bound”, which means that all those big muscles stiffen you up compared to the non-muscular population. The truth is that any sort of activity can make you more flexible than somebody that sits around all day. Sitting shortens your hip flexors and overstretches your back muscles. Lifting weights encourages good posture and stretches out the muscles which will help lead to flexibility.
The authors admit that research on stretching can be found to hold up basically any theory. I can not really speak to whether my lifting makes me more flexible or not, though. I run more than I lift, and I stretch often. I am naturally a very flexible person to begin with. I have friends that have lifted and run just as much as I have though that can barely get their hands past their shins, which strikes me as not quite right.