Can a flight to get FBI fingerprinted for job clearances be listed as a work expense?

No.  The cost of the fingerprinting and clearance process appears to be an unreimbursed employee expense and as such it would not be deductible.  Prior to the Tax Cut and Jobs Act, unreimbursed employee expenses were deductible, but such expenses were subject to various conditions and limitations.  Now, such expenses are no longer deductible.

Your move from SC to PA is also not deductible.  As it did with unreimbursed employee expenses, the TCJA changed the rules relating to moving expenses.  Now, unless you are active duty military and meet certain requirements, moving expenses are no longer deductible.

Here is a link to a TurboTax article regarding moving expenses which you might find helpful.  

Are Moving Expenses Tax Deductible