Using twisted bilayer γ-graphyne (TBGY) as an example, we show that it is possible to create multiple flat bands in carbon allotropes without the requirement of a specified magic angle. The origin of the flat bands can be understood by a simple two-level coupling model. The narrow bandwidth and strong localization of the flat band states might lead to strong correlation effects, which make TBGY a good platform for studying correlation physics. On the basis of the two-level coupling model, we further propose that the width and extent of localization of flat bands can be tuned by an energy mismatch Δ E between the two layers of TBGY, which can be realized by either applying a perpendicular electric field or introducing a heterostrain. This allows continuous modulation of TBGY from the strong-correlation regime to the medium- or weak-correlation regime, which could be utilized to study the quantum phase transition.