Three things should be considered first.
- Size of USB drive
- Type of Distribution
We will use an application called UNetbootin to install the Linux into the flash drive. We can let the program download a distro or select the image file(.iso) of an already downloaded distro. Download UNetbootin here: http://unetbootin.sourceforge.net/ and install it.
Whole article here: How to Install Portable Linux Into Usb Drive | ProgrammerFish - Everything that's programmed!