Yes, you can save contacts from LinkedIn with InTouchApp Extension for Chrome & Firefox directly to your phone.
Before you proceed, you need InTouchApp installed on your phone & InTouchApp Extension installed on Chrome or Firefox. Learn more.
How to Save Contacts from LinkedIn to my phone?
Step 1 - Log in to your LinkedIn account
Step 2 - Open the LinkedIn Connect's profile whose contacts details you want to save
Step 3 - Click on See contact info
Step 4 - Then click on Save Contact button. (Note: if you do not see Save Contact button, your extension is not working as expected.
Step 5 - Select if you want to add as Add New Contact or Add to Existing, fill in the details and click on Save Contact button.