  We propose a model for magnetic noise based on spin-flips (not
electron-trapping) of paramagnetic dangling-bonds at the
amorphous-semiconductor/oxide interface. A wide distribution of spin-flip times
is derived from the single-phonon cross-relaxation mechanism for a
dangling-bond interacting with the tunneling two-level systems of the amorphous
interface. The temperature and frequency dependence is sensitive to three
energy scales: The dangling-bond spin Zeeman energy delta, as well as the
minimum (E_min) and maximum (E_max) values for the energy splittings of the
tunneling two-level systems. We compare and fit our model parameters to a
recent experiment probing spin coherence of antimony donors implanted in
nuclear-spin-free silicon [T. Schenkel {\it et al.}, Appl. Phys. Lett. 88,
112101 (2006)], and conclude that a dangling-bond area density of the order of
10^{14}cm^{-2} is consistent with the data. This enables the prediction of
single spin qubit coherence times as a function of the distance from the
interface and the dangling-bond area density in a real device structure. We
apply our theory to calculations of magnetic flux noise affecting SQUID devices
due to their Si/SiO_2 substrate. Our explicit estimates of flux noise in SQUIDs
lead to a noise spectral density of the order of 10^{-12}Phi_{0}^{2} {Hz}^{-1}
at f=1Hz. This value might explain the origin of flux noise in some SQUID
devices. Finally, we consider the suppression of these effects using surface
passivation with hydrogen, and the residual nuclear-spin noise resulting from a
perfect silicon-hydride surface.
