In this work we study the e^{+}e^{-}\to\phi K^{+}K^{-} reaction. The leading order electromagnetic contributions to this process involve the \gamma*\phi\ K^{+}K^{-} vertex function with a highly virtual photon. We calculate this function at low energies using R\chi PT supplemented with the anomalous term for the VV'P interactions. Tree level contributions involve the kaon form factors and the K*K transition form factors. We improve this result, valid for low photon virtualities, replacing the lowest order terms in the kaon form factors and K*K transition form factors by the form factors as obtained in U\chi PT in the former case and the ones extracted from recent data on e^{+}e^{-}\to KK* in the latter case. We calculate rescattering effects which involve meson-meson amplitudes. The corresponding result is improved using the unitarized meson-meson amplitudes containing the scalar poles instead of the lowest order terms. Using the BABAR value for BR(X\to \phi f_{0})\Gamma (X\to e^{+} e^{-}), we calculate the contribution from intermediate X(2175). A good description of data is obtained in the case of destructive interference between this contribution and the previous ones, but more accurate data on the isovector K*K transition form factor is required in order to exclude contributions from an intermediate isovector resonance to e^{+}e^{-}\to \phi\ K^{+}K^{-} around 2.2 GeV.