I had the same problem, the only way to make a static library is to open MobileVLCKit.xcodeproj, switch to TVVLCKit and build. You get libTVVLCKit.a and headers.
I compiled MovileVLCKit as static libTVVLCKit.a. Video playback works good if I use UIView with small dimensions. But if you set the dimensions to Full HD. Playing lags (CPU usage cca 110%).