Does the Cingular flip model number 3620 phone have the call block/unblock feature?

RTFM!
Read The 'Fabulous' Manual!

att.com/support_static_files/manuals/ATT_Cingular_Flip_M3620.pdf

I think,

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11.4 Call

2) Send My Number: you can send your number 'Set by Network', 'Hide ID' and 'Send ID'.
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does the job.