Typical structures of monitoring systems (MSs) that are used in urban complex objects (UCOs) (such as large industrial facilities, power facilities, and others) during the post-accident period are combined with the technologies of flying sensor networks (FSNets) and flying edge networks (FENets) (FSNets and FENets); cloud/fog computing and artificial intelligence are also developed. An FSNets and FENets-based MS, composed of one of the Advanced Air Mobility (AAM) systems classes, which comprise main and virtual crisis centers, fleets of flying sensors, edge nodes, and a ground control station, is presented and discussed. Reliability and survivability models of the MS for the UCOs, considering various operation conditions and options of redundancy, are developed and explored. A tool to support the research on MS reliability, survivability, and the choice of parameters is developed and described. Crucially, this paper enhances the technique for assessing systems using the multi-parametrical deterioration of characteristics as a class of multi-state systems. Problems that may arise when using FSNets/FENet-based AAM systems are discussed. The main research results comprise a structural basis, a set of models, and a tool for calculating the reliability and survivability of FSNets/FENet-based AAM systems, with various options for distributing the processing and control resources between components, their failure rates, and degradation scenarios.