Kongregate’s Statistics API are not only compatible, but there are already blocks in the Design Mode palette for using them. There’s an article that discusses them on Stencyl’s website that may help you.
Achievements are a different story – Kongregate decides which games get achievements and implements them on their side using any statistics that you report (such as the player’s score) using the above Statistics API. The only thing you can do is produce as good of a game as possible and then report statistics and hope they decide to make them into Achievements. You can find more details on them within Kongregate’s Developer Center.