I really want to improve my flatpicking skills, and I kind of like bluegrass and country music, but I dont know much songs in these genres. I am looking for some simple-medium level songs in these styles, which would really improve my flatpicking skills, while having fun learning songs and also making my repertoire bigger. I appreciate any suggestions
Well, there are so many... Are you looking for traditional bluegrass-type songs that you can sing and accompany, or for bluegrass instrumentals?

For an excellent source of instrumentals in tab, let me suggest the "Flatpicker's Hangout" site, which has a pretty large collection of standard tunes in both tab and "TEF" format: