Is there a syntax to specify multiline code snippets in Google (Hangouts) Chat?

If it's a single line, you can use it between single back quote.

`Hello World`

Google (Hangouts) Chat only supports basic (not rich nor full Markdown) formatting. For your specific inquiry, use pairs of triple backticks, i.e.,

```
Hello
World
```

For this and other formatting directives, see either the consumer help page (for end-users), or the simple messages page (for developers) in Google's documentation.