You need three things to get fast charging: 1. A two amp charger, 2. A two amp capable cable, and 3. An App to confirm you are getting the maximum current. The Note comes with a two amp charger as do the chargers for most tablets. Check the specs on any after market chargers you buy or use.
Cable current capacity varies widely, and USB 3.0 doesn't guarantee a high charging speed. I've had very good luck with the Monoprice 6-Feet Premium USB to Micro USB Charge & Sync Cable, Black (109762) available at Monoprice or Amazon for about $6. It's only a USB 2.0, however I like that because I can use it on any device.
Lastly you need an application to tell you if you are getting the correct amperage. There's a nice free app available at the Google Play Store called Galaxy Charging Current Lite which works fine on the Note 3. I found that I get 1,200 to 1,800 milliamps charging from the Monoprice cables I referenced or with the original cable supplied with the phone. The 1,800 ma charging rate occurs during the initial stage of charging, but after a short time it settles down to 1,200. I've gotten as low as 450 ma with other cheap cables I have used.
So for starters, put the the charging current app on your phone and see what you're getting currently. If you are already getting 1,200 ma, then you are fine. If you're not, you need to get some new cables and/or a new charger.