Hi julieda,
I understand that when an iPhone 6 Plus is plugged into an HDTV, the TV flashes. Let's see if we can get it sorted out with some additional troubleshooting that has already been done.
I would take a look at the article below and look of the troubleshooting sections for the Apple Digital AV Adapters. It will have you check the additional cables that are connected to the adapter. I would even to go as far as trying another adapter if one is available.
About Apple Digital AV Adapters for iPhone, iPad, and iPod touch
https://support.apple.com/en-us/HT202044
If you encounter an issue using the Apple Digital AV Adapter or VGA Adapter:
- Disconnect and reconnect the adapter from the iOS device and display.
- Connect directly to the TV, projector, or external display using a known-good VGA or HDMI cable.
- Remove any VGA or HDMI extension cables or converters.
- Note that accessories that convert a VGA or HDMI signal to other video formats (DVI, Composite, Component) are not supported.
- Ensure that you are using the latest version of iOS. Some Apple Digital AV Adapters require iOS 5.1 or later.
When using an Apple Digital AV Adapter manufactured before early 2012 with iPad (3rd generation), you may see the "This accessory is not supported" alert. Dismissing the alert will allow you to use the adapter.
For optimal performance, you may need to adjust the video resolution or settings for your display. If your display offers an "auto detect" or "factory default" setting, you may be able to use these options to optimize video resolution and display.
Have a good day
