my brand new iPhone 6s will not turn on. when plugged into charger the Apple icon appears then goes to black screen then repeats.

Are you sure you have a new device? the iPhone 6s was released September 2015.

Anyways, if your device turns on but gets stuck during start up

You might see the Apple logo or a red or blue screen for a long time during startup. Try these steps:

1. Connect your device to a computer and open iTunes. If you don't have a computer, you can borrow one, or go to an Apple Retail Store or Apple Authorized Service Provider for help.
2. While your device is connected, force it to restart.

• On an iPhone 7 or iPhone 7 Plus: Press and hold the Sleep/Wake and Volume Down buttons at the same time.
• On an iPhone 6s and earlier, iPad, or iPod touch: Press and hold the Sleep/Wake and Home buttons at the same time.

3. Don't release when you see the Apple logo. Keep holding until you see the recovery mode screen.

4. When you get the option to restore or update, choose Update. iTunes will try to reinstall iOS without erasing your data.

iTunes will download the software for your device. If it takes more than 15 minutes, your device will exit recovery mode and you'll need to repeat steps 2 and 3.

Just a guess.. but your 'brand new' phone was discontinued 2 years ago (32/128GB versions) or 4 years ago (16/64GB versions). it's possible then that the battery sat dead so long that it can't hold adequate charge and needs to be replaced?