I don't think you can do this with gmail. Gmail insists on sending a confirmation code to a new forwarding address. Since you can't access email sent to your kindle email address, you won't be able to complete gmail's authorization process.
I solved this problem by setting up an email address at gmx.com that I only use with Calibre. Gmx does not require authorization to forward to an address. I send all of my news from Calibre to gmx and use the gmx filters to forward the news to the various kindles.
I use the same gmx account as the outgoing email server in Calibre This speeds up emailing the news since the delay Calibre places between outgoing email via gmail is eliminated.
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