You have a project which has got some SW requirements to run (e.g.: a specific version of Apache, a version of PHP, an instance of a MySQL database and a couple of other pieces of software).
You have already discovered Vagrant, so your virtual environment is all setup. You can create boxes out of your configuration files and cookbooks.
You have also understood the advantages of a Continuous Integration system such as Jenkins.
Now you would like to combine these two worlds (Vagrant and Jenkins) to get the perfect Continuous Integration Environment. To be more specific, you would like not to install the SW required by your project on the machine running Jenkins, but you would like to use the virtual environment provided by Vagrant to periodically build your project on the top of it. The CI software (Jenkins) will build the Vagrant box for you and build and test your project on the top of it.
How would you setup your environment to achieve this?
it is a good solution for build system, my suggestion:
Probably you can take a look at veewee, which can create vagrant box on fly.
Here is the Make CI easier with Jenkins CI and Vagrant for my guideline for this suggestion.