ShinobiCharts doesn't provide these sorts of animations out of the box - it provides entry and exit animations for entire series. However, it doesn't mean that this isn't possible. You could create this effect a few ways:
1) You could use our streaming API to start with an empty chart and append data to a series. You can see an example of this in our AppendData sample packaged with our framework.
2) You could simply start with an empty chart, update your datasource and reload your chart every time you want to add some points. Extending upon this, Sam Davies wrote a great blog post on how to implement custom animations with our chart using Facebook's Pop framework. You might be able to create some quite cool effects using this!
I hope the above helps.