We present a robust method for synthesis of aligned, single-walled carbon nanotube (CNT) "flying carpets" from nanostructured alumina flakes. Roll-to-roll e-beam deposition is utilized to produce the flakes, and hot filament chemical vapor deposition is utilized to grow dense, aligned carbon nanotubes from the flakes with remarkably high CNT yields. The flakes are captured inside a mesh cage and freely suspended in the gas flow during growth. Optical characterization indicates the presence of high quality, small diameter single-walled carbon nanotubes.