Experimental and theoretical results are reported for fiat diffusion flames adjacent to a spinning fuel disk in on oxidizing atmosphere. Disk-shaped flames are observed. the radii of which increase or decrease with time, depending on whether an appropriate Damkohler number is large or small. Experimentally, initially large flame disks expand at sufficiently high Damkohler numbers, while at sufficiently small Damkohler numbers, initially small flame disks contract, as predicted by theory. A stability map is derived theoretically in a plane of the Damkohler number and the flame-disk radius normalized by a diffusion length scale, showing regimes of disk growth and shrinkage.