Chaotica's native parameter format is .chaos. Saving and loading of Chaos files can be done using File > Save World (ctrl+s) and File > Open World (ctrl+o).
Chaos files include imaging settings, so you can preserve things like curves. The .chaos format is intended to hold much more information than .flame, so the conversion is one-way (you can not export from Chaotica back to Apophysis).
For now, Chaotica only saves in .png. This can be accessed via File > Save Image.