Does the blinking light have a certain shape? Is it blinking at regular intervals or is it random? It doesn't occur when you're on the Roku's home screen or other menus? Does the blinking occur on your screen with TV channels or other video sources?
First, I would remove the HDMI cable (if you're using an HDMI cable) from both the Roku and TV. Next, remove power from the TV, Roku and any other connected devices for at least 30 seconds. Reconnect the HDMI cable. Then, power the TV back on and any other connected devices, and finally, power on the Roku. (Edit: It might also be worth trying a different HDMI cable that is rated for 4K 18Gbps throughput).
If this doesn't work, the next thing you might want to try is a factory reset. Note that after the reset you will have to relink your Roku account to your Roku Express and sign into your wireless network. You'll also have to sign back in to any apps that require a sign-in. Here's a link
indicating how to do a factory reset. Here's a link
detailing how to link your account to your Roku. You don't have to reselect the apps you had installed on your Roku as these are saved in your account and will be reinstalled on your Roku when you link to your Roku account.
If none of these steps eliminate the blinking light on your screen, it's quite likely your Roku Express is defective.