How Much Current Draw From Speakers/Amplifier?
According to the docs the efficiency is reasonably high, I believe 89% for 8Ω is mentioned. 

If you want to be able to drive the speakers at full power continuously:

Total power [Watt] = number of channels × power per channel 

P = 2 × 2.8 = 5.6 W

Supply current drawn for the speakers alone would be:

Current [Ampère] = Power [Watt] / Voltage[Volt]

I = P / V = 5.6 / 5 = 1.12 A

Accounting for efficiency, you are looking at 1.12 / 0.89 = 1.26A. This is with 8Ω load, efficiency with a 4Ω load will be worse.

The datasheet for the amp states another 5.5 mA supply current.

The datasheet for the codec lists power draw of up to 60 mA.

Total current draw would be at least 1.35A at full load. 

However there are quite a few assumptions here and you really want some headroom for unforeseen things. Maybe you want to add a indicator LED? I did not account for an SD card or another microcontroller to control things. In practice you mustn't aim for a power supply that can't do at least 1.5A and I'd probably pick a 2A power supply as it is good practice to not push a power supply to its spec'd limits.