Whereas the rigid nature of standard thermoelectrics limits their use, flexible thermoelectric platforms can find much broader applications, for example, in low-power, wearable energy harvesting for internet-of-things applications. Here we realize continuous, flexible thermoelectric threads via a rapid extrusion of 3D-printable composite inks (Bi2Te3 n- or p-type micrograins within a non-conducting polymer as a binder) followed by compression through a roller-pair, and we demonstrate their applications in flexible, low-power energy harvesting. The thermoelectric power factors of these threads are enhanced up to 7 orders-of-magnitude after lateral compression, principally due to improved conductivity resulting from reduced void volume fraction and partial alignment of thermoelectric micrograins. This dependence is quantified using a conductivity/Seebeck vise for pressure-controlled studies. The resulting grain-to-grain conductivity is well explained with a modified percolation theory to model a pressure-dependent conductivity. Flexible thermoelectric modules are demonstrated to utilize thermal gradients either parallel or transverse to the thread direction.