I bought 256 GB flash drives to back up my info on my MacBook Pro. However the software says it’s compatible with Mac iOS X version 10.9. My MacBook Pro is V 10.7.5. Can I still use these flash drives with confidence they will save my information?

If the drive is properly formatted you can use it with any Mac.

However, you should not use any flash drive as a long term or backup storage device. They are notoriously fragile and prone to suddenly failing with no warning, and they are slow.

I recommend you buy an inexpensive USB hard disk drive or solid state drive (SSD) and use that with Apple's Time Machine backup software to backup your stuff. Time Machine is built in and installed with macOS. Not only can you use a TM backup to recover individual files when needed, but it is also possible to restore the entirety of the macOS on a machine that experiences failures.

Back up your Mac with Time Machine - Apple Support