Yes you can but if you have a lot of files, a flash drive won't back it all up. If you only need to back up 32GB-64GB for example, you could back it up on the flash drive. However, anything bigger isn't sensible for flash drives; you're better off getting an external hard drive. Also, it's not a long-term storage option––it can corrupt easily or be lost.
There's a lot to choose from when it comes to buying a flash drive. The most important thing to consider is size. The whole point of a USB drive is to store lots of data in a small space, so think about what kinds of files you'll want to house on your flash drive. Movies and music take quite a bit of space, so if you're carrying your whole entertainment library with you, you'll want a big thumb drive – at least 16GB. Books and other text-based documents require relatively little storage space, so people like students and working professionals using Microsoft Office would be happy transferring Word documents or Excel files with as little as 1GB of space. On the other hand, if you are using photo or music editing software, you'll want a USB flash drive with lots of storage capacity to transfer graphic and music files.