Hi, I'm new to this too, so I'm no expert but:
To install on your local machine, you don't need to use kitematic, you could just use the reaction Command Line Interface:
This will pull the source code locally so you can see it on your machine. But if you want to make custom plugins / themes you will then need to do more. The guys at reaction seem to suggest building a docker image from the local code changes. But if you need to work with other developers this may not work. You can also clone fork reactioncommerce/reaction to github/bitbucket and create your own dockerfile on docker hub and deploy a custom build like that.
Im not sure about deploying on DO but the docs are here:
Im going to write a tutorial on deploying with Amazon Elastic Beanstalk, so if you want code for that I can help with that.