We study recent observations of propagating fluctuations in a prominence foot with Hinode Solar Optical Telescope ( SOT ) high-resolution observations in Ca II and H \alpha emission which we identify as nonlinear fast magnetosnic waves . Here we analyze further the observations of propagating waves and flows with Interface Region Imaging Spectrograph ( IRIS ) Mg II slit jaw images , in addition to Hinode/SOT Ca II images . We find that the waves have typical periods in the range of 5 - 11 minutes and wavelengths in the plane of the sky ( POS ) of about 2000 km , while the flows in narrow threads have typical speed in the POS of \sim 16 - 46 km s ^ { -1 } . We also detect apparent kink oscillations in the threads with flowing material , and apply coronal seismology to estimate the magnetic field strength in the range 5-17 G. Using 2.5D MHD we model the combined effects of nonlinear waves and flows on the observed dynamics of the prominence material , and reproduce the propagating and refracting fast magnetosonic waves , as well as standing kink-mode waves in flowing material along the magnetic field . The modeling results are in good qualitative agreements with the observations of the various waves and flows in the prominence foot , further confirming coronal seismology analysis and improving the understanding of the fine scale dynamics of the prominence material .