We report on the design, fabrication and measured performance of hierarchical sinuous-antenna phased arrays coupled to cryogenic lithographed detectors for millimeter-wave astronomy. This architecture allows for dual-polarization wideband sensitivity with a beam width that is approximately frequency-independent. This solves a common problem with multichroic pixels, which is that the beam width varies with frequency and causes suboptimal sensitivity in most frequency bands. We achieve a variable pixel size, i.e., a multiscale focal plane, by creating phased arrays from neighboring lenslet-coupled sinuous antennas, where the size of each array is chosen independently for each frequency band, so that the effective pixel size scales with wavelength. Our devices consist of arrays of hemispherical lenses coupled to lithographed wafers, which integrate transition-edge-sensor (TES) bolometers with superconducting sinuous antennas and microwave circuitry including band-defining filters. The design can be straightforwardly modified for use with non-TES lithographed cryogenic detectors such as kinetic inductance detectors (KIDs). We have demonstrated frequency-independent beam widths from a three-level hierarchical sinuous-antenna phased array over a 3:1 bandwidth. Additionally, we have demonstrated several other microwave components such as a 4:1 broadband 180-degree hybrid that can simplify the design of future multichroic focal planes including but not limited to hierarchical phased arrays. We discuss the development of a 4-band hierarchical phased array that is scalable in the sense that it can tile a wafer for use in a current or upcoming experiment.