What is the easiest way to scale a data science project based on scikit stack?
You generally don't.  Scikit-learn is primarily aimed to help new data scientists quickly get comfortable with data science

That being said, some strategies for scaling are discussed here: http://scikit-learn.org/stable/modules/scaling_strategies.html

This includes using out-of-core models, reducing data size with PCA, and various incremental learners

Besides that, your best bet is to use a beefier computer

Also, remember that once a model is trained, it can be pickled and shared.  Training/testing is usually the time/cpu consuming process.  So, once you have a model, you should be able to implement it on machines less beefy than the train/test machine