Can I transfer xbox 360 game progress from one profile to another?

No. Nothing can be transferred between accounts.

Actually you can genious pay attention to the last line:

Can I transfer content from one Xbox LIVE account to another?

No. Content licenses are stored in the Xbox 360 console rather than in the Xbox LIVE account.

To enable someone else's Xbox LIVE account to use your content licenses, you must download your Xbox LIVE profile and then transfer your content licenses to that person's Xbox 360 console.

•To download your Xbox LIVE profile to a different Xbox 360 console, see Download, move, or delete your Xbox LIVE profile.

•To transfer a content license from one Xbox 360 console to another, see Can I transfer a content license from one Xbox 360 console to another?

After you've downloaded your Xbox LIVE profile and transferred your content licenses to another Xbox 360 console, the content can be used by all the profiles on that console.

To let someone else use the content license, you must download your Xbox Live profile to their Xbox 360 console. Then, transfer your content licenses to that Xbox 360 console.

• To download your Xbox Live profile to a different Xbox 360 console, see
  Download your Xbox Live profile to a different Xbox 360 console or redownload it.
  
• To transfer a content license from one Xbox 360 console to another, see above section,
  
  Can I transfer a content license from one Xbox 360 console to another?

After you transfer your content, other profiles can use the content on that console.

There are a few games that will allow you to transfer save files to other profiles although I believe you will be unable to earn any achievements from those. Otherwise, nothing can be transferred between profiles.

Hi there,

I'm afraid there is no way to transfer anything from one account to another account. The Xbox Account is linked to the Microsoft account and can not be transferred, same for progress in games etc.