Is it possible to post files to Slack using the incoming Webhook?

I am trying out the Slack's API using the incoming webhook feature, posting messages works flawlessly, but it doesn't seem to allow any file attachments.

Looking through I understand I have to use a completely different OAuth based API, but creating more tokens just for the purpose of uploading a file seems odd when posting messages works well, is there no way to upload files to slack with the incoming webook?

No, its is not possible to upload files through an incoming Webhook. But you can attach image URLs to your attachments with the image_url tag.

To upload files you need to use the Slack Web API and the files.upload method. Yes, it requires a different authentication, but its not that complicated if you just use a test token for all API calls.