Flat bands are of significant interest due to their potential for strong energy confinement and their ability to facilitate strongly correlated physics such as unconventional superconductivity and fractional quantum Hall states. When topology is incorporated into flatband systems further enhance flatband mode robustness against perturbations. Here, we present the first realization of doubly degenerate topological flatbands of edge states in chiral-symmetric strained graphene. The flatband degeneracy stems from the merging of Dirac points, achieved by tuning the coupling ratios in a honeycomb lattice with newly discovered twig boundary conditions. The topology of these modes is characterized by the nontrivial winding number, which ensures their robustness against disorder. Experimentally, two types of topological edge states are observed in a strained photonic graphene lattice, consistent with numerical simulations. Moreover, the degeneracy of the topological flatbands doubles the density of states for zero-energy modes, facilitating the formation of compact edge states and providing greater control over edge states and light confinement. Our findings underscore the interplay among lattice geometry, symmetry, and topology in shaping doubly degenerate topological flatbands. This opens new possibilities for advancements in correlated effects, nonlinear optical phenomena, and efficient energy transfer in materials science, photonic crystals, and quantum devices.