AFAIK the 2013 Air already has flash memory. I'd check the reasons for the beachballing first. Let malwarebytes run once. Make an Etrecheck run and see what it spits out.
If it was me, I'd erase the hard drive and reformat it with a fresh copy of OSX. Then I'd re-install all required programs, e.g. Office, etc. Get it back to its pristine, brand new condition and hopefully wipe out any HD/software issues it may have developed over the years. But that's just me.