A simple way to take screenshot on iPhone 6 (and other iPhones and iPads) is to press and hold the Home and Sleep button at the same time. But if for any reason your Home button is not responsive enough, you need to do as follows to take screenshot on iPhone 6 without using the Home button:
1. Make sure the Assistive Touch button is enabled and you can see the white floating button on the screen. (Click here to learn how to enable Assistive Touch, or simply go to Settings>General>Accessibility>Assistive Touch and turn the feature on)
2. Now go to the view you want to capture the screen, tap the floating assistive button to open the popup menu
3. Tap the Device button, followed by the More button and finally tap the Screenshot button to capture the screen on iPhone 6 and other iOS devices.
** Note that, you may bring the Screenshot button to the top level using the Customize Top Level Menu in the Assistive Touch menu. It enables you to take a screenshot on iPhone 6 in 2 steps: tap the assistive touch button followed by the screenshot button.