Can I move photos from Dropbox on my iMac back to my new iPhone 6?

Install the Dropbox app on your phone. Log in to your account. Tap photos at the bottom of the screen. Tap the photo to be saved. Tap the share icon(box with arrow). Tap save image. The photo gets saved in Photos.

When you download the photos they are also put into the Recents Album which is the new name for photo stream.

An alternative to drop box is Airdrop. Airdrop can be a lot quicker in most cases.

Here's a link with more information about Airdrop.

iOS: Use AirDrop to wirelessly share content