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In the vanadium oxyfluoride compound(NH$_4$)$_2$[C$_7$H$_{14}$N][V$_7$O$_6$F$_{18}$] (DQVOF), the V$^{4+}$ (3d$^1$,$S=1/2$) ions realize a unique, highly frustrated breathing kagome latticecomposed of alternately-sized, corner-sharing equilateral triangles. Here wepresent an $^{17}$O NMR study of DQVOF, which isolates the local susceptibilityof the breathing kagome network. By a fit to series expansion we extract theratio of the interactions within the breathing kagome plane, $J_\triangledown /J_\vartriangle = 0.55(4)$, and the mean antiferromagnetic interaction$\bar{J}=60(7)$~K. Spin lattice, $T_1$, measurements reveal an essentiallygapless excitation spectrum with a maximum gap $\Delta / \bar{J}=0.007(7)$. Ourstudy provides new impetus for further theoretical investigations in order toestablish whether the gapless spin liquid behavior displayed by DQVOF isintrinsic to its breathing kagome lattice or whether it is due to perturbationsto this model, such as a residual coupling of the V$^{4+}$ ions in thebreathing kagome planes to the interlayer V$^{3+}$ ($S=1$) spins.

Nature of the spin liquid ground state in a breathing kagome compound studied by NMR and series expansion