We demonstrate the emergence of slow-light in dual-periodic dielectric one-dimensional photonic crystals with self-similar features at different length scales. Specifically, using numerical modelling, we explore self-similar photonic crystals which are formed as effective combinations of dual periodic stacks of dielectric layers and show that the emergent photonic band diagram can be widely designed by different structural parameters. The width and the position of bandgaps can be designed to work over a wide range of bands and frequencies. The proposed design also leads to the emergence of flat bands and major slow-light regimes, with possible group refractive index of light as large as 103 and in a range of bands.