I believe NY FLI refers to New York Family Leave Insurance, and it should be posted to Box 14 of your W-2. Box 20 of the W-2 is for posting a Locality, or a city code, and this does not apply.
This does sound like an oversight, and you should once again bring it to your employer's attention. The only tax consequence of NY FLI is the potential to increase the federal deduction for state income tax. If you don't itemize your deductions, it will not change anything on either your federal or state tax return.
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