Currently Amazon does not ship the Echo to Singapore.

The only way to get it is through freight forwarders.

Option 1 : Amazon direct

You pay all shipping and other charges. Approx US 180 + 50 SGD shipping

Sign up for Borderlinx

There are other websites that do this but I find them to be the most reliable and quick.

Create an Amazon Account

Not sure what you are doing if you dont have an account :)
Create here

Set your address to your Borderlinx account

Everyone's address is unique so be sure to use yours!

Buy the Echo and checkout as normal

Remember to set your borderlinx address as your shipping address

Option 2 : Carousell

You pay a premium and there needs some element of trust. Approx 300 SGD

https://sg.carousell.com/search/products?query=echo%20amazon