Screen flickering on your laptop when you plug in an external one is usually a compatibility or driver issue rather than actual hardware damage. Before you panic, try the simple stuff first: swap out your HDMI cable (sometimes it's literally just a bad connection), and then restart your laptop with the monitor already plugged in. If that doesn't help, go into Windows/Mac display settings to make sure your resolution and refresh rate are properly configured. Sometimes the laptop and external monitor don't agree on these settings and that causes the flickering.
Another thing to check: it might be your graphics driver that's out of date. You can go to your graphics card manufacturer's website (Intel, AMD, Nvidia depending on what you've got) and download the latest driver version. That usually fixes this kind of problem without you needing to return the monitor.
If it's still flickering after all that, try plugging the Dell into another device just to verify it's not the screen itself that has an issue. Like a different HDMI port, another laptop, whatever. If it does the same thing everywhere, then you can think about filing a claim with Dell. But I'd bet good money it's just a driver or cable thing you can sort out quickly.