  We present a study of the decays B^{+-} --> D K^{+-} with D mesons
reconstructed in the K+pi-pi0 or K-pi+pi0 final states, where D indicates a D0
or a anti-D0 meson. Using a sample of 474 million BBbar pairs collected with
the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC we
obtain R^{+} = (5^{+12}_{-10}(stat) ^{+2}_{-4}(syst))\times10^{-3} and R^{-} =
(12^{+12}_{-10}(stat) ^{+3}_{-5}(syst))\times10^{-3}, from which we extract the
upper limits at 90% probability: R^+<23\times10^{-3} and R^-<29\times10^{-3}.
Using these measurements, we obtain an upper limit for the ratio rB of the
magnitudes of the b --> u and b --> c amplitudes r_B<0.13 at 90% probability.
