We present an initial feasibility summary of a femtosecond synchrotron radiation x-ray source based on a flat-beam rf gun and a recirculating superconducting linac that provides beam to an array of undulators and bend magnets. Optical pulse durations of <100 fs are obtained by a combination of electron pulse compression, transverse temporal correlation of the electrons, and x-ray pulse compression. After an introduction and initial scientific motivation, we cover the following aspects of the design: layout and lattice, ultra-fast x-ray pulse production, flat electron-beam production, the rf gun, rf systems, cryogenic systems, collective effects, photon production, and synchronization of x-ray and laser pulses. We conclude with a summary of issues and areas of development that remain to be addressed.