So I am deploying a OpenStack private cloud in my business. As I understand from research the OpenStack project was created by RackSpace and that their own cloud platform uses OpenStack.
So my question is would it be possible to migrate or move images/servers from my private OpenStack cloud to RackSpace OpenStack public cloud?
I don't believe you can directly migrate the images using any of Rackspace's built-in tools (at least I don't see such an option readily advertised) -- Check with your rackspace account manager though, they might be able to do this for you as a consulting service (or they may have a tool that just isn't well-advertised).
Another option if you anticipate splitting your environment between the private cloud and the Rackspace hosted cloud would be to use a tool like puppet / chef / radmind to deploy your environment -- You could then manage both environments with these tools, and you would gain a number of other advantages that configuration management software brings.
At this moment in time, no.
Rackspace does not support uploading of images to their platform at this time, this may change in the future, especially as Rackspace complete their implementation of Openstack (still some legacy Slicehost stuff left over).
Another project worth mentioning is the aeolusproject
This also offers alternatives to chef via the Audrey component, where the post build tasks are defined as XML.
Your RAX account manager may point you in the direction of their new DevOps Rackers.
Rackspace are rolling out a new platform called CheckMate that will aid customers to deploy application stacks rather than simply just servers. Here's a great slidepack from a presentation at the Texas Linux Fest last year. They're now contributing heavily to the Heat solution. Something you can potentially use in your private and public cloud.
Similarly, have you tried out Scalr or RightScale? Both enable you to build cross-cloud server images (sort of). Might be too late for your existing images today but if you proceed like this, you can deploy in either of your clouds using the same tooling.
No technical answer I'm afraid but thanks for listening!!
If you're open to using commercial software for this task and running Xen or ESX(i), check out https://cloudpath.racemi.com/
As mentioned, I'm not sure there's any option to deploy data from your Openstack private to Rackspace public cloud. However, I've done something like this from my Openstack based cloud to AWS to minimize size and costs, using a third party vendor. I did cloudendure, it went well, obviously you could browse for different vendors in various costs. It is very efficient and quick method, though.