Completed Chapter 1 saves are supposed to appear in Chapter 2 automatically, but somehow the two games are hosted on different subdomains of kongregate.com which prevents the feature from working as intended.
Hopefully this can be fixed, but until then here's how to continue in Chapter 2:
1. Use the "Save to File" button on the main menu in Chapter 1 to create worlds-end-chapter-1.sav
2. Select "New Game" in Chapter 2's main menu, click "Load from File" and select the .sav file you just created