Alarm lights flash after installing battery and driving

Couple questions on this. Are you the original owner? Do you know if the theft system is bypassed?

If sounds like the ECM is ignoring the theft light except now that the battery was disconnected and then reconnected, it forced a reboot of the immobilizer.

Basically, I suspect we have an issue with the key that you are using due to it not being an OEM and now that the battery has been replaced, the bypass program was erased.

Here is a guide that will help with disabling it, but I doubt this is going to work in your specific issue:

https://www.2carpros.com/articles/how-to-reset-a-security-system

If this doesn't then we need to check for codes and find out what the issue is. The common codes are below but let's start with this and find out what is there. Thanks