How do I move my Health data from one device to another?
iCloud will back up your health data on your iPhone so you can restore your health data to a new device or to your device if it fails or needs to be wiped. 

If you don’t use iCloud, iTunes also backs up health data but only if you select "Encrypt iPhone Backup".

When you do a "Restore from Backup" on your iPhone 6, select the encrypted backup you just made. Your health data will then come across along with all other backed up data. 

If you do not encrypt your backup (as I did) and you have already "moved on" with your iPhone 6 with new apps and data, well then, that is another question that I am trying to find the answer to, as the above will not help you much.

See http://support.apple.com/en-us/ht5262