I hope you have viewed this video:
Now, about the antenna connection. I'm not happy with the way that you have prepared the bare end of your coax in the picture. At 2.4 Ghz, the way you have your ground braid pigtailed out should never be done and you will suffer a considerable loss of communication range doing it this way. If you want good range, we must do it differently and this will take some minor surgery for a good antenna cable connection. I hope your soldering skills are up to it.
The linked video begins with a closeup of the board, and I think it is the same as your board. This closeup shows a strange antenna connection that I think is bad. The true antenna feedpoint for the Bluetooth transceiver (the point where a 50 ohm transmission line should be connected) is on the little submodule, the little board with the 8645 chip on it (see image below). It's feedpoint feeds an existing antenna on the submodule of a type called Planar Inverted F Antenna, which is the gold colored trace in the shape of an inverted F. The maker of the board has put a jumper wire from an abitrary point on the inverted F to their J2 connection point, and this jumper wire shows an utter lack of consideration for RF transmission line principles. I suspect it has been done this way because they don't give a damn about optimizing the communication range. In order for your coax connection to work properly, we are going to have to connect it up to the feedpoint, and we are going to have to disconnect the existing inverted-F antenna. You cannot have two antennas on one connection without a proper power splitter, which we don't have here.
As you can see, there are no convenient pads for this purpose, and this is where the surgery comes in. You see that little white chip component at the feedpoint. I suspect this is a capacitor, but we have to check to make sure. Our coax connection will be at the antenna side of that capacitor. This involves using a fine knife (xacto or equivalent) to cut the gold trace as shown in the attached image (second one below). The remaining little patch of gold trace still connected to the capacitor will be the connection pad for the center conductor of our coax. However, don't connect this up just yet. With the really small coax that we are dealing with here, we always must attach the ground braid first and then the center conductor. This avoids stressing the center conductor wire, which is very fine and can break easily. In order to solder the coax braid, we have to surface mount it. This means that we prepare the coax as shown in another attached image, tin the exposed braid with solder, then surface mount the braid down to some exposed ground plane very close to the feedpoint. This will be tricky as there is not much to connect to. I will provide a drawing showing the best place to do this in a later post. Until then, the third image is a rough attempt to show you how the coax will dress. The black is coax, the green color is coax with the outer jacket removed and the braid exposed. The grey is the braid cut away exposing the dielectric, and the yellow is the center conductor wire exposed. Soldering the ground braid down to the board is tricky and should be done with a fine iron.