How long does it take to get a phone shipped to you after filing a theft and loss claim?

With whom did you file a theft & loss claim? If you had AppleCare+ on your device and filed a claim with them, this link may be helpful:

File a claim if you have AppleCare+ with Theft and Loss coverage - Apple Support

I’ve copied the pertinent part below:

To check the status of your claim, you might need this information:

• Your claim number or Apple dispatch ID
• The serial number or IMEI of your iPhone
• The purchase date of your AppleCare+ with Theft and Loss plan, which you can find at mysupport.apple.com

Then it’s a question for AIG.