Everything flowers, pretty much, but sometimes not so often under current conditions, or not obvious to human eyes. Is it really a vine (that is, twining or clinging) or a leggy suckering shrub? No matter what it is, the control options won't vary too much - dig dig dig, most likely.
Nope it's definitely a Honey Suckle Vine AKA Lonicera japonica http://www.invasive.org/eastern/images/1536x1024/2307154.jpg Regards Chris