The iPad Air supports third-party batteries without issues. The question is if the replacement battery is good or not. However, I have to say that the red flash is quite worrisome. This is a symptom we’ll often see with deeper, logic board related issues, specifically the NAND.
So take a step back, double check your work, look for any damage to the flexes, connectors or the surrounding area on the logic board. I would also re-install the original battery (assuming it was good enough to boot the device prior to replacement) to see if you have the same symptoms. If the original battery allows the iPad to boot properly, then consider the replacement battery to be either bad or deeply uncharged (in which case you can let it charge over night). If the original battery no longer boots the device properly, then you probably damaged something during the repair.