When you are using LinkedIn app on your mobile web then you would have to check whether you are in private browsing or whether there are cookies in your web browser. Read on to know how to troubleshoot on iPhone iOS 8.0 and above:
Go to your iPhone's home screen > tap on Settings > scroll the page down and tap on Safari.
Now, tap on Block Cookies > tap on From third parties and advertisers.
Then tap on Safari which is at the top.
Scroll the screen down and then tap on Advanced.
Now, open the Safari app > then find the Tabs icon in the lower right and tap on it.
This would display all of Safari's open pages and 3 options at the bottom. Tap on Private > then find a grey box around the word Private when private browsing is enabled.
If you are prompted to close or keep all opened tabs choose the latter.
Now, go to www.linkedin.com and try signing in.