Cutting the long story short, Kindle app is not available in Google Play Store (Android Marketplace) when you access the Store from Singapore. But there's an easy way out. Follow these simple steps:
1. Download the app (.apk file) to your computer from the following page:
Download Kindle for Android
Note: I couldn't access that page directly from the phone.
2. Transfer this file to your Android device. I transferred the file via Bluetooth.
3. Install the app and enjoy reading on Kindle.
Just for your information, I installed the app on my Samsung Galaxy S3, and so far it has been working well. Let me know your experience.
