  Flares in the X-ray afterglow of gamma-ray bursts (GRBs) share more
characteristics with the prompt emission than the afterglow, such as pulse
profile and contained fluence. As a result, they are believed to originate from
late-time activity of the central engine and can be used to constrain the
overall energy budget. In this paper, we collect a sample of $19$ long GRBs
observed by \emph{Swift}-XRT that contain giant flares in their X-ray
afterglows. We fit this sample with a version of the magnetar propeller model,
modified to include fallback accretion. This model has already successfully
reproduced extended emission in short GRBs. Our best fits provide a reasonable
morphological match to the light curves. However, $16$ out of $19$ of the fits
require efficiencies for the propeller mechanism that approach $100\%$. The
high efficiency parameters are a direct result of the high energy contained in
the flares and the extreme duration of the dipole component, which forces
either slow spin periods or low magnetic fields. We find that even with the
inclusion of significant fallback accretion, in all but a few cases it is
energetically challenging to produce prompt emission, afterglow and giant
flares within the constraints of the rotational energy budget of a magnetar.
