Can I capture photos in Raw mode on iPhone 6 without have to pay for a 3rd party app?
The built-in camera app in iOS doesn't support capturing RAW photos. You'll have to rely on a 3rd party app.

Since you are not looking for a paid app, you can download VSCO a free app that supports capturing photos in RAW mode.

OTOH, on the paid front, Halide Camera is a highly regarded app by photography enthusiasts and power users alike.

Note: No affiliation whatsoever. The answer is based on personal experience and ratings on the App Store.