To access your existing Blink system from a second device, all you need to do is download the Blink app from either the Apple App Store or Google Play Store. Once downloaded, use the Sign In option and enter in the same email address and password that you used to set up your Blink system on the other device. You will not need to set up the system again, as it is all tied to that account. After you've done that, you'll be able to access your Blink system from multiple devices.
If you do not see your system after signing into the second device, double check the email address on the original device to ensure that you have entered in the correct email address. To do this, tap on the curtain menu in the top left corner of the screen. A menu will slide out and your email address will be displayed at the very top.