Hello there, Aimy.
It sounds like you are having an issue downloading a previously purchased app onto you're new iPhone 6. The following Knowledge Base article goes over how to redownload and speaks about in-app purchases as well:
Download past purchases from iTunes - Apple Support
On an iPhone, iPad, or iPod touch
- Tap App Store.
- On an iPhone or iPod touch: Tap Updates, then tap Purchased.
On an iPad: Tap Purchased.
- Scroll to find the app that you want to download.
- Tap the Download icon . After the app downloads, you can open it from your Home screen.
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Some in-app purchases like game currency or hints are consumable, which means that they run out as you use them. You can only restore non-consumable purchases. Learn more about in-app purchases.
Thanks for reaching out to Apple Support Communities.
Cheers.