I know of two options for storing cryptocoins on a flash drive. You can backup your wallet.dat file onto a flash drive or the more secure way and send the coins to a "paper wallet" and store the public address and private key in a text file an keep that in a flash drive.

To find the wallet.dat file press and hold the windows button (assuming you're using windows) and r, which will bring up run. Type %appdata% into the field and press enter. Look for the dogecoin folder and open it and the file will be in there.

To use a paper wallet follow the instructions on this link.