First of all to get an API Key for middleware from Linkedin, you must first have an account with Linkedin. If you don’t have an account you can create one at https://www.linkedin.com. Then fill up your account details to become a member. Thereafter follow the following steps to generate your API key-
You will be lead to the following page:
Fill in all the required details necessary and then save.
You will be lead to the following page displaying the message that you have successfully created your application with all the informations required, i.e. your API key and your Secret Key, and you are done.