Amorphous photonic materials offer an alternative to photonic crystals as a building block for photonic integrated circuits due to their shared short-range order. By using the inherent disorder of amorphous photonic materials, it is possible to design flexible-shaped waveguides that are free from restrictions of photonic crystals at various symmetry axes. Effects of disorder on photonic crystal waveguide boundaries have examined before, and it is shown that flexible waveguides with high transmission are possible by forming a wall of equidistant scatterers around the defect created inside amorphous material configuration. Based on this principle, waveguides with various flexible shapes are designed and fabricated for planar circuit applications. A silicon-on-insulator (SOI) slab with random configuration of air hole scatterers is used. The amorphous configuration is generated through realistic Monte Carlo simulations mimicking crystalline-to-amorphous transition of semiconductor crystals via an assigned Yukawa potential to individual particles. The design parameters such as average hole distance, slab thickness and hole radius are adjusted so that the waveguide is utilizable around 1550 nm telecommunications wavelength. Such waveguides on slab structures are characterized here and the level of randomness and band gap properties of amorphous configurations are analyzed in detail. These efforts have the potential to lead easier design of a wide range of components including but not limited to on-chip Mach-Zehnder interferometers, splitters, and Y-branches.