The flashing "double click" instruction has fooled many first-time iPhone X users, causing them to awkwardly start tapping the screen. What it is trying to tell you is to double click the side button, which will invoke Face ID to make sure you have permission to download apps. This is simply to avoid downloads due to accidentally tapping the "Get" button and then having Face ID automatically give permission to download because it sees you.
To force quit an app on iPhone X, open your App Switcher by swiping up from the bottom of the screen halfway then pausing, or turn your swipe to the right when you reach mid-screen. Find the app you want to kill then long press on it until a red "-" button shows up in the top left corner of the app. Tap it to quit the app.
On the iPhone X you don't have to pull up the App Switcher to switch between apps, there is a more convenient way to get between recently used apps. Simply swipe from right to left at the very bottom of the screen. Your apps will be arranged chronologically, with the most recently used app showing up first.
While testing has shown that Face ID is slightly slower than Touch ID, you can speed it up simply by swiping up as soon as you pick up your iPhone X. This will start the process a lot earlier than if you just pick up the phone, stare at the screen and wait for the lock icon to unlock before swiping up to reveal your Home screen. Also, toggle off "Require attention for Face ID" so you it doesn't have to actually verify that you are looking at it to unlock.
The iPhone X introduces some major design changes including, most notably, the absence of a physical Home button. While this can understandably take some time getting used to from an ergonomic perspective, the lack of a Home button also means no more Touch ID, which was an incredibly convenient security feature not just for unlocking your iPhone, but for accessing apps with sensitive data as well. For this reason and for even stronger security, Apple introduced a new biometric scan with the iPhone X - Face ID.