Your contact wil be stored on the Galaxy S3, or in the Google cloud.
iCloud is the Apple cloud so the contacts on your Galaxy S3 wont be stored there.
Basically you have moved from one platform (Android on your S3) to Apple (iOS on your iPhone 6) and they are compatible.
You realty need to export your contacts from your Galaxy and import them in to your iPhone 6.
Search for a web site that explains how to move from Android to iOS.
Here is one
https://support.apple.com/en-gb/HT201196