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lst = {{r1, θ1, ϕ1}, {r2, θ2, ϕ2}, {r3, θ3, ϕ3}}

Thread[Y[k, q, Transpose@lst]]

{r1^(-1 - k) SphericalHarmonicY[k, q, θ1, ϕ1],
r2^(-1 - k) SphericalHarmonicY[k, q, θ2, ϕ2],
r3^(-1 - k) SphericalHarmonicY[k, q, θ3, ϕ3]}