Its perfectly possible to back up your data files to flash drives.
Flash drives are often of limited capacity, and whilst they may be OK for backing up some data, they're rarely of sufficient capacity to contain system (disc Images)
Several USB type external hard drives are useful for this and are inexpensive to buy these days.
Remember that back ups often merely create a false sense of security unless kept on separate media and with at least 3 different copies, all verified as reproducible and accurate and with at least one kept offsite on removable media.
As it's generally not a good idea to back up your "junk" files and any virus or malicious (or merely undesirable code) it may be wise to do a spot of "housekeeping" and run a few on demand type malware scanners of good repute to ensure that your computer's system is as clean as reasonably possible before your back ups are routinely started.
Remember with disc images (using for example free disc imaging tools like Macrium Reflect Free) you will be copying everything on your disc/partition and that includes the good and the bad....hence the need for the "housekeeping"
Post back if you need any further information on any of this.