I published two scripts on Powershell gallery in order to automate the deployment of a SharePoint Framework solution:

The first script basically collects automatically the bundle publishing it on Office 365 CDN, while the second across the SharePoint ALM API is able to upload the package of the solution in the App Catalog. Everything you need to do is running the command:

Save-Script -Name VSTS.DeploySPFxToAppCatalog -Path <SPFx root>

you will find in the SPFx root a Powershell script that you can use for deploying the solution on test or production by using VSTS for example.

The solution is also available on GitHub at the following URL where is also described how to configure the continuous integration and deployment on Visual Studio Team Services: https://github.com/giuleon/AutomatedDeploymentForSPFx

Read also these two related articles: