We report the linear viscoelasticity of densely grafted poly(styrene)-block-poly(ethylene oxide) (PS-b-PEO) diblock bottlebrush block copolymers (dbBB) of equal mass fraction over a wide range of backbone degree of polymerization (N-bb = 21-119). The difference in side chain length (PS M-n = 2.9 kg/mol, PEO M-n = 5 kg/mol) produces an asymmetry between the molecular shape of the two blocks despite their equal mass fractions. The dbBBs rapidly self-assemble into lamellar morphologies upon thermal annealing. Increasing N-bb results in an increase of domain spacing from d(0) = 29 to 90 nm. In the microphase separated melt state, dbBBs are thermorheologically simple and remain unentangled up to large molecular weight (M-w > 500 kg/mol). Oscillatory shear rheology data shows distinct power law relationships analogous to critical gels across a wide range of time scales. The viscoelasticity is expressed by a dual power law relaxation time spectrum H(tau), consisting of relaxation processes at short (n(1)) and long (n(2)) time scales. Scaling on short time scales (n(1) approximate to 0.83) is attributed to the cooperative mobility of internal slip layers (ISLs) confined within the microphase separated domains. Slipping is facilitated by a high concentration of free chain ends in the middle of each domain. Longer time scales (n(2) approximate to 0.67) are dominated by the microphase separation, which is globally disordered. The results suggest a weakly percolating structure with rapid dynamic rearrangements of bottlebrushes within the PS/PEO interface.