Whispering gallery mode resonator (WGMR) microspheres yield highly structured optical spectra that are extremely sensitive to their environment and are of intense interest for use in a variety of sensing applications. Many efforts to leverage the unique sensitivities of WGMRs have relied on stringent experimental requirements to correlate specific spectral shifts/changes to an analyte/stimulus such as (1) precise positional knowledge, (2) reference spectra for each microsphere, and (3) high mechanical stability. Consequently, these factors can hinder adequate mixing or incorporation of analytes and can create challenges for remote sensing. This work describes a continuous flow technique for measuring whispering gallery mode (WGM) spectra of dye-doped microspheres suspended in solution and an accompanying analysis scheme that can extract the local refractive index without a priori knowledge of the microsphere size and position and without a reference spectrum. This measurement technique and analysis scheme was shown to accurately measure the refractive index of a range of alcohol and saline solutions down to a few thousandths of a refractive index unit (RIU). Additionally, a spectral clustering algorithm was applied to the fit results of two batches of microspheres suspended in water and was able to accurately assign spectra back to either batch of microspheres.