Are FSA contributions already calculated into the amount in Box 1 of the W2?

No. Since medical FSA contributions are typically not taxable, they are omitted from Box 1.  They are not required to be reported elsewhere, though they may be reported in Box 14 as other. 

See: What is a Flexible Spending Account (FSA)? for more information.

If you have a salary reduction agreement to put money in a medical FSA, it should be removed from your box 1 wages by your employer.  If you are concerned the wages were not removed, you need to talk to your employer. 

If you have a salary reduction agreement to put money in a dependent care FSA, it should be removed from your box 1 wages and include in box 10.  You need to complete the dependent care interview to give the name of the caregiver and your qualifying expenses.