Airport Extreme AC flashing amber and AP Utility can't find it.

A flashing amber status LED typically indicates that either a configuration setting is incorrect or that the base station has not be fully configured yet. It normally does not indicate a failed device ... although anything is possible.

I would suggest that you perform a "factory default" reset on your AirPort Extreme to see if you can both access it again and be able to configure it for your networking needs. This type of reset will return the base station back to its original factory default settings. Which is to perform as an Internet router that will broadcast an unsecured wireless network with a network name of something like: Apple Network NNNNNN. Your Mac or iPhone should now be able to find this network so that they can connect to it. Once connected, just use the AirPort Utility to configure it a required. Please post back your results.

Try (again) temporarily connecting your Mac directly to one of the LAN (opposing arrows) port using an Ethernet cable. Can your Mac's AirPort Utility "see" the base station now?

If not, it may be possible that your new Extreme may be defective and should be returned for a replacement.

There are two different flashes of the amber.. during a reset it will flash amber quickly.. about 1/2 sec..

During a normal setup it will flash amber at about 1sec intervals.

The fast flash if it never stops means the reset is jammed.. double check that the switch is not stuck.. People do over pressure it and result in damage.

But it can also indicate a fault in the flash RAM on the unit.. which is a fault beyond home user.. it needs to go back to apple for replacement.