Lightning Aura Components – Chart.js Not Working with Locker Service Enabled Org: How to Fix

This seems unrelated to the JS library you are using. What is most likely happening is the following: a parent component is trying to call a child helper using the verbose approach:

var concreteHelper = cmp.getConcreteComponent().getDef().getHelper();

We want to remove access to this API because it exposes the complex internal structure of the component. It's hard to test, and hard to maintain.

You need to remove the .getDef().getHelper() and replace it with something else. The trick is to declare a method on your concrete component:

<aura:method name="myMethod" action="{!c.myMethodHandler}"/>

And call it from the super component:

component.getConcreteComponent().myMethod();

In Lightning, every level of inheritance creates a component. This is a better pattern, since the helper is not part of the public API of a component like a method. You can define the method on an interface and ensure every instance abides to the contract, something that the .getDef().getHelper(); was not allowing.

You just forgotten to declare the variable zipFile, change the line

zipFile = new JSZip();

to this line:

var zipFile = new JSZip();

also I will recommend you to use the Salesforce Lightning CLI to check this kind of issues, its a heroku command line tool that check for this errors.

Follow this steps to install Salesforce Lightning CLI: https://developer.salesforce.com/docs/atlas.en-us.lightning.meta/lightning/cli_intro.htm

UPDATE: In my personal org I tested the code you provided with a few modifications in an aura application and it worked fine. Here is the code:

App:

<aura:application >
    <ltng:require scripts="/resource/jszip/jszip.min.js" afterScriptsLoaded="{!c.onPress}"/>
</aura:application>

Js controller:

  ({
        onPress : function(component) {
            var packageXml = '<?xml version="1.0" encoding="UTF-8"?>' + 
                '<Package xmlns="http://soap.sforce.com/2006/04/metadata">' +
                '<version>35.0</version>' +
                '</Package>' ;

            var zipFile = new JSZip();
            zipFile.file('package.xml',packageXml,{base64: 'true'});
            var data = zipFile.generateAsync();
            alert(data);
        }
    })

I downloaded the last version (3.0.0) of jszip from their site and had the issue that the method generate() is deprecated, so I changed it to generateAsync() as is suggested in the upgrade guide.