When viewing a contact profile, a user may not see the "Send a Campaign" button near the top of the page.
The "Send a Campaign" button only appears in the contact profile when a campaign has previously been sent to a list. The user needs to be granted permission to view the list(s) that the contact has received campaigns through.
The account user must have permission to access the list a campaign was sent to in order to view that campaign. If the contact was only ever sent campaigns from lists which the user is restricted from viewing, the user will not see the "Send a Campaign" button.