We present measurements of the elliptic flow, \(v_2\), as a function of transverse momentum (\(p_T\)), pseudorapidity (\(\eta\)), and centrality in $d$$+\(Au collisions at \)\sqrt{s_{_{NN}}}=\(200, 62.4, 39, and 19.6 GeV. The beam-energy scan of \)d$$+\(Au collisions provides a testing ground for the onset of flow signatures in small collision systems. We measure a nonzero \)v_2\( signal at all four collision energies, which, at midrapidity and low \)p_T\(, is consistent with predictions from viscous hydrodynamic models. Comparisons with calculations from parton transport models (based on the {\sc ampt} Monte Carlo generator) show good agreement with the data at midrapidity to forward (\)d\(-going) rapidities and low \)p_T\(. At backward (Au-going) rapidities and \)p_T>1.5\( GeV/\)c\(, the data diverges from {\sc ampt} calculations of \)v_2\( relative to the initial geometry, indicating the possible dominance of nongeometry related correlations, referred to as nonflow. We also present measurements of the charged-particle multiplicity (\)dN_{\rm ch}/d\eta\() as a function of \)\eta\( in central \)d$$+\(Au collisions at the same energies. We find that in \)d$$+\(Au collisions at \)\sqrt{s_{_{NN}}}=\(200 GeV the \)v_2\( scales with \)dN_{\rm ch}/d\eta\( over all \)\eta\( in the PHENIX acceptance. At \)\sqrt{s_{_{NN}}}=\(62.4, and 39 GeV, \)v_2\( scales with \)dN_{\rm ch}/d\eta\( at midrapidity and forward rapidity, but falls off at backward rapidity. This departure from the \)dN_{\rm ch}/d\eta$ scaling may be a further indication of nonflow effects dominating at backward rapidity.