You can use datmo/kaggle:python to be able to run kaggle projects with jupyter notebook. After pulling the image, you can use code like this in the shell:
docker run --rm -it -p 8888:8888 -v ~/.:/home/ datmo/kaggle:python 'jupyter notebook'
This mounts the local directory onto the container having access to it.
Then, go to the browser and hit https://localhost:8888, and when I open a new kernel it's with Python 3.5. I don't recall doing anything special when pulling the image or setting up Docker.
You can find more information from here.
You can also try using datmo in order to easily setup environment and track machine learning projects to make experiments reproducible. You can run datmo task command as follows for setting up jupyter notebook,
datmo task run 'jupyter notebook' --port 8888
It sets up your project and files inside the environment to keep track of your progress.