Making use of this loophole is most likely against Amazon's TOS. Remember that the data going through your Kindle is tied to a unique ID, and that if you do this, Amazon is most likely going to know. You are going to take the risk of potentially bricking your device.
This is not my idea... Credit goes to a Chinese guy called dgejal at bbs.duokan.com. I am just translating his post into English.
I was actually debating if I should publicize this to a greater extent, given Amazon does watch...
Well, here's how you can browse any web site over KT's 3G connection.
1. Go to Settings, Reading Options, Social Networks, make sure your don't have your Twitter account linked. Unlink it if you do.
2. Select Link Account under Twitter.
3. The Twitter login page will show up. Don't login here, instead, click the Twitter icon at upper left corner, it will bring you to the Twitter homepage.
4. Login with your Twitter account now. It won't go back to Kindle's Manage Your Social Networks page.
5. Send a tweet with the URL you wait to go. For instance, tweet "www.google.com"
6. Click on Home to force a refresh. You should see your last tweet now.
7. Click on the URL
You are free now... One catch, some web site gave me 'Can not connect' error, not sure why.
Fine print: I hold zero responsibility on whatever action Amazon might take on your device...