The only the admin and control have the authority to delete a campaign in LinkedIn from there own account using the campaign menu setting in Linkedin
Steps to Delete A Campaign In Linkedin
1.Select the campaign you would like to delete using the Linkedin campaign menu
2. Go to campaign Settings > Campaign Settings. If you’re using the simplified navigation Linkedin menu, you will need to click the Linkedin More Tools button at the top of the sidebar.
3. Then you need to select the Tool Options button and then choose the Delete Campaign from the Linkedin menu
4.Finally enter the Campaign URL and then click the delete Linkedin Campaign to confirm. There’s not a way to restore data after deleting Campaign.
If you do not see the delete button in the LinkedIn campaign page, the main reason is that you do not have any permission to delete the campaign. in these manners, you need to contact the account owner to delete the LinkedIn campaign