Flow coefficients (v2 and v3) are measured in high-multiplicity p+Au, d+Au, and He3+Au collisions at a center-of-mass energy of sNN=200 GeV using the STAR detector. The measurements utilize two-particle correlations with a pseudorapidity requirement of |η|< 0.9 and a pair gap of |Δη|>1.0. The primary focus is on analysis methods, particularly the subtraction of nonflow contributions. Four established nonflow subtraction methods are applied to determine vn, validated using the HIJING event generator. vn values are compared across the three collision systems at similar multiplicities; this comparison cancels the final-state effects and isolates the impact of initial geometry. While v2 values show differences among these collision systems, v3 values are largely similar, consistent with expectations of subnucleon fluctuations in the initial geometry. The ordering of vn differs quantitatively from previous measurements using two-particle correlations with a larger rapidity gap, which, according to model calculations, can be partially attributed to the effects of longitudinal flow decorrelations. The prospects for future measurements to improve our understanding of flow decorrelation and subnucleonic fluctuations are also discussed.