I followed the suggestion of someone on the Kindle forum and did a basic 2X2 cable every fifth row.

Cast on 64 stitches using Judy’s Magic cast-on. Work in the round on DPNs. Do a 2X2 cable every fifth row. Do a right cross for the first set of cables, then five rounds do a left cross. Repeat this until the cozy is the right length for the Kindle. Cast off half the stitches and knit in garter stitch for an inch and a half. Make a button hole in the middle of the next row, knit another inch, then cast off.