Google chrome is the most used web browser in the world. In Incognito mode the browser will not store any kind of history, cookies, cache, and extensions(by default if you didn't change the setting).

 Once you close the browser everything will be gone and nothing will be saved. You will be automatically signed off (if you may signed into a website). However downloads and bookmarks may appear.

 While your browser’s Incognito Mode is an excellent way to keep local users from viewing your browsing activities, but it doesn’t do much when it comes to protecting you from the other online users, your Internet service provider, websites you visit , or the government and law enforcement.

 it can not protect from any kind of attacks or theft even it can not hide your IP at all,
if you are login with your Gmail id in incognito mode then all our information will be saved in Google Server, Hence it is not that safe.

 But how to do Safe Browsing?

 VPNs are the best way to keep your IP address hidden.  A VPN’s encrypted connection provides protection for your online activities. While your Internet service provider or government may be able to tell that you’re connected to a VPN provider, they have no way of knowing where your travels take you from there. All of your online activities are protected by the layer of encryption.

 or you can user the Tor Browser, it makes your online browsing traffic anonymous through layers of encryption, But it may result in slow connection.