How Can I Fully Wipe Data Off a Phone?

I've heard that with flash storage, nothing is really wiped off.
If someone uses the right tool or program, they could pull "erased" data off the phone.

And I know this is a whiteHat/Ethical-Hacking forum, but calling up Apple support, they didn't seem to know what I was talking about, or any way (other than system reset, which I have my doubts on) to permanently wipe data. So I wanted to ask the WhiteHat community for a more security and technical view of this.

My question is, how can I wipe it permanently?

(the back story to this is that I've switched to a new phone carrier, they gave me an iPhone, I've got some data on it (thankfully nothing too sensitive), but after realizing that they signed me into the wrong plan, they told me they will cancel the plan, given that I return the said iPhone (iOS9), and they'll give me a new iPhone (same OS, same model/type/storage)

And before anyone starts saying "Why are you on iOS? Android is better for development", let me clarify that my old phone (before the switch) is an Android phone, and I love it very much thank you.

So, how can I permanently wipe data off my iPhone so that no one with the right tools can pull up that data again

Thanks