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Abstract The dispersion measure of fast radio bursts (FRBs), arising from the interactions with free electrons along the propagation path, constitutes a unique probe of the cosmic baryon distribution. Their constraining power is further enhanced in combination with observations of the foreground large-scale structure and intervening galaxies. In this work, we present the first constraints on the partition of the cosmic baryons between the intergalactic medium (IGM) and circumgalactic medium (CGM), inferred from the FLIMFLAM spectroscopic survey. In its first data release, the FLIMFLAM survey targeted galaxies in the foreground of eight localized FRBs. Using Bayesian techniques, we reconstruct the underlying ∼Mpc-scale matter density field that is traced by the IGM gas. Simultaneously, deeper spectroscopy of intervening foreground galaxies (at impact parametersb_⊥≲r₂₀₀) and the FRB host galaxies constrains the contribution from the CGM. Applying Bayesian parameter inference to our data and assuming a fiducial set of priors, we infer the IGM cosmic baryon fraction to be $f_{\mathrm{igm}}={0.59}_{-0.10}^{+0.11}$and a CGM gas fraction of $f_{\mathrm{gas}}={0.55}_{-0.29}^{+0.26}$for 10¹⁰M_⊙≲M_halo≲ 10¹³M_⊙halos. The mean FRB host dispersion measure (rest-frame) in our sample is $〈{\mathrm{DM}}_{\mathrm{host}}〉={90}_{-19}^{+29}\mathrm{pc}{\mathrm{cm}}^{-3}$, of which $〈{\mathrm{DM}}_{\mathrm{host}}^{\mathrm{unk}}〉={69}_{-19}^{+28}\mathrm{pc}{\mathrm{cm}}^{-3}$arises from the host galaxy interstellar medium (ISM) and/or the FRB progenitor environment. While our currentf_igmandf_gasuncertainties are too broad to constrain most galactic feedback models, this result marks the first measurement of the IGM and CGM baryon fractions, as well as the first systematic separation of the FRB host dispersion measure into two components: arising from the halo and from the inner ISM/FRB engine.