||You'll need scripting for the loop. I'd probably think about structuring it like this to make it more managable:
1. Create a layer for your counties feature class, include all features, see Make Feature Layer tool.
2. Create a function that takes a FIPS code as a parameter. It then defines a new temporary layer based on your counties, see Select Layer by Attribute tool. It then copies the selected features of that layer to a new shapefile, see Copy Features tool.
3. Once you have that supporting function worked out, then focus on the "driver" loop. You'll open up a select cursor on the counties layer, loop through each record, retrieve the FIPS value for that record, and call your "SaveFIPStoShapefile" function.
Hope that at least gives you some ideas,