I use EAC to rip and tag and use WMP to find artwork. Can't say it's the best way but I have been doing it a while so it doesn't take long, and I find WMP finds decent versions of the cover art.
I rip each album to a separate folder in my FLAC directory, WMP usually figures out that this is an 'album'. Various artist albums can have problems, but if you sort by song, then click the column top that is file locations, the various artists on a single album will appear in a row, then shift-click or ctrl-click to highlight them all, then right-click 'find album info'
If WMP doesn't have find the album art, I find a decent cover, save it, then drag it into WMP.
Don't forget if Squeezecenter already knows about the music and you add album art later, it won't show up unless you do a 'clear library and rescan everything'.
WMP seems to keep it's own tagging system, so you will need another program for FLAC tag management that will work with Squeezecenter. Your tag management program should be able to imbed the artwork in the FLAC file automatically if you choose, then it will show up if you drag single songs to a portable device.
My system is probably needlessly tedious, but I really don't trust programs that 'fix' everything automatically. I recall many complaints when earlier itunes versions would redo your whole file structure by default. Ouch!
Good Luck!