  We develop a theory of macroscopic resonant tunneling of flux in a
double-well potential in the presence of realistic flux noise with significant
low-frequency component. The rate of incoherent flux tunneling between the
wells exhibits resonant peaks, the shape and position of which reflect
qualitative features of the noise, and can thus serve as a diagnostic tool for
studying the low-frequency flux noise in SQUID qubits. We show, in particular,
that the noise-induced renormalization of the first resonant peak provides
direct information on the temperature of the noise source and the strength of
its quantum component.
