We investigate the linear viscoelastic behavior of poly(styrene)-block-poly(ethylene oxide) (PS-b-PEO) AB di-block brush copolymer materials over a range of volume fractions and with side-chain lengths below entanglement molecular weight (PS M-n similar to 3.5 kg/mol and PEO M-n similar to 5 kg/mol). The high chain mobility of the brush architecture results in rapid microphase segregation of the brush copolymer segments, which occurred after mild thermal annealing. Master curves of the dynamic moduli were obtained by time-temperature superposition (tTS). The reduced degree of chain entanglements leads to a unique liquid-like rheology similar to that of bottlebrush (BB) homopolymers, even in the microphase-segregated state. The microphase-segregated domains were found to align at exceptionally low strain amplitudes (gamma = 0.01) and mild processing temperatures as confirmed by small-angle X-ray scattering (SAXS). Domain/grain orientation occurred readily at strains within the linear viscoelastic regime (LVR) without noticeable effect on the dynamic moduli. This interplay of high molecular mobility and rapid phase segregation contrasts the viscoelasticity of brush block copolymers (BBCP) compared to conventional linear block copolymer (LBCP) analogues and opens up new processing possibilities of BBCP materials for a wide range of nanotechnology applications.