There is not a dedicated line for reconsideration of Capital One Credit Card applications. You will need to call one of the customer service numbers or the credit card application line.
How do I ask for credit card reconsideration?
How to contact reconsideration. The easiest way to contact your card issuer's reconsideration department is to simply call their main customer service line and ask to be transferred to reconsideration. Sometimes you'll get a contact number with your denial letter.
When should you call a reconsideration line?
You can usually wait up to 30 days to call into reconsideration about your application but I do not recommend waiting that long. There are plenty of reports of Chase pulling your credit report again if you wait near that long. So I would call in as soon as I got a rejection or the 7 to 10 day message.