If you want to increase your flexibility, follow the advice of the experts - perform your resistance exercises with good technique through a full range of motion, and you will actually increase your flexibility.
Of course, adding flexibility training to your workouts, either as part of your cool down, or later in the day, will have numerous benefits (e.g. improved performance, reduced risk of injury, quicker recovery from workouts) and help ensure that you maximize the benefits of the hard work you do.