The manufacturing process starts with designing the mold for the frame. During design phase 3d software (such as SolidWorks) is used to determine how thick the frame needs to be ie. many layers of carbon composite each part of the frame needs. Normally the frame is glued together from several separate parts (as many as seven) so a mold is needed for each part. The mold has two halfs and a hole for fitting the balloon.
Essentially frames are made mixing polymer epoxy with fiber composite materials. The fibers form a weave that makes up the distinctive carbon fiber patterns. Depending on the width the weaves are called 3k and 12k. The former is finer meshed and the latter wider. The weaves do not necessarily translate to specific riding characteristics. More depends on the epoxy used.
Often times manufacturers advertise that they use Toray carbon from the japanese chemical company. Since the company produces several different types of carbon composites the name Toray does not really tell all that much about the characteristics of the frame. Sometimes there is a mention about using lighter T1000 type. As far as the fibers go at least on one of the pics taken at the FlyBike factory a cardboard box of SkyFlex prepreg from SK Chemicals in Korea is shown so that is at least one brand used in production.
The actual building starts when a composite cutter (such GGT from Gerber) is used to cut preform pieces of fiber composite. Since the fibers are unidirectional the orientation of layers applied on top of each other is important for reaching the desired characteristics for each part of the frame. The pieces of the kit are simply applied into the mold in the designated order and then the resin is applied on top.
To cure the construction a balloon is filled inside the mold and the whole is put into an oven (180F) to dry the epoxy resin. Once ready the frame is assembled from the pieces by gluing them together with resin. Some strips of fibers may be layered on top to hide the connection points. In this phase internal cabling and holes for things like bottle holders are added. Once dried up the frame is taken to be painted and laquered. The carbon monocoque frame is ready for use.