Flame spray pyrolysis (FSP) provides an advantageous synthetic route for LiNi1-x-yCoxMnyO2 (NCM) materials, which are one of the most practical and promising cathode materials for Li-ion batteries. However, a detailed understanding of the NCM nanoparticle formation mechanisms through FSP is lacking. To shed light on the evaporation of NCM precursor droplets in FSP, in this work, we employ classical molecular dynamics (MD) simulations to explore the dynamic evaporation process of nanodroplets composed of metal nitrates (including LiNO3, Ni(NO3)2, Co(NO3)2, and Mn(NO3)2 as solutes) and water (as solvent) from a microscopic point of view. Quantitative analysis on the evaporation process has been performed by tracking the temporal evolution of key features including the radial distribution of mass density, the radial distribution of number density of metal ions, droplet diameter, and coordination number (CN) of metal ions with oxygen atoms. Our MD simulation results show that during the evaporation of an MNO3-containing (M = Li, Ni, Co, or Mn) nanodroplet, Ni2+, Co2+, and Mn2+ will precipitate on the droplet surface, forming a solvent-core-solute-shell structure; whereas the distribution of Li+ within the evaporating LiNO3-containing droplet is more even due to the high diffusivity of Li+ compared with other metal ions. For the evaporation of a Ni(NO3)2- or Co(NO3)2-containing nanodroplet, the temporal evolution of the CN of M-OW (M = Ni or Co; OW represents O atoms from water) suggests a "free H2O" evaporation stage, during which both CN of M-OW and CN of M-ON are unchanged with time. Evaporation rate constants at various conditions are extracted by making analogy to the classical D2 law for droplet evaporation. Unlike Ni or Co, CN of Mn-OW keeps changing with time, yet the temporal evolution of the squared droplet diameter indicates the evaporation rate for a Ni(NO3)2-, Co(NO3)2-, or Mn(NO3)2-containing droplet is hardly affected by the different types of the metal ions.