AFAICT, Linode doesn't offer that, and they probably won't. Amazon's been ahead in this arena for awhile, and will probably keep that lead for the forseeable future. EDIT: Apparently they do have an API which would cover a decent variety of use cases.
What's sad is the number of people that migrate over to Amazon because it's the done thing, without realizing what they're paying for (and that they're not utilizing the unique features of EC2).
I believe there may have been other incidents.
That said, I still have a number of services running happily on Linode. :)
And it's just a continued pattern of incompetence and cover up.
While perhaps not entirely as mature and full featured as AWS's offering, Linode does offer an api with which you can script creation/initialization of test servers.
They also offer something called StackScript, that to me looks like some kind of configuration management script. https://www.linode.com/stackscripts/
But they do not make it very easy to spin up / down new instances. Setting aside the API, they bill you for a full month for a new instance as soon as you create it. True, you get a pro-rated credit if you delete it earlier but this is awkward and I think it only pro-rates by the day.
And StackScripts kinda sorta work, but they are hard to write/debug and are not portable. It's a pretty weak offering.
Another important aspect is ability to easily transfer raw data into an analysis tool, like Red Shift. Google also excels here with their Compute Engine and Big Query.
While it is cool that AWS has a ton of services they offer, I do not like the vendor lockin that comes with AWS services. I think it is generally a better strategy to go with something OpenStack based. That way you can use your own hardware and dynamically provision new nodes in "the cloud" with companies like HP, RackSpace, and others. With modern day virtualization, running your own hardware can often be much cheaper and much more performant than AWS.
Digital Ocean does do metered billing, and their API is very sweet & simple.
Obviously the API isn't as mature - but it is going in the right direction