  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.
