You can read about a COBRA FSA here.
It seems to me that having a COBRA FSA wouldn't make sense unless you had contributed most of the money while still employed, but had not spend much of it, because the COBRA FSA lets you continue to spend the amount already contributed (i.e., the pre-tax amount). To answer your question ("What's the purpose of having an FSA while on COBRA if you cant deduct from your gross income? "), this is why you might want to do it, rather than forfeit the money you already contributed.
Otherwise, I don't see why you would want to do it. A good HR department would walk you through this as part of the exit process.
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