How do I add up analogue inputs to average them?

I assume you want to do this using a microcontroller, right? What controller do you use?
You can do it your way, this will average packets of 20 values each. I.e. you will get one output for every 20 inputs.

Another approach is a moving average (or rolling average). This will give you an output for every input, also averaged over e.g. 20 values. The advantage is that this method will allow you to react faster to change in input, quickly detect trends etc.

 

The ACS712 has a built-in filter. You can select the amount of noise suppression by changing the filter capacitor on pin 6. No need to average on the mcu, but possible, of course.
Which mcu will you use? many of today's mcus have built-in ADCs, so you wouldn't need a separate ADC, unless you want an accuracy much higher than what a built-in ADC of an mcu can offer.