Power problems

The first problem is that the LEDs on the right end of the strip don't get enough power because of the resistance in the strip. This causes color difference. This is easily fixed by powering it from the right also.

Flickering

Second problem is flickering at lower brightness levels. The first thing I could think of was adding a couple of capacitors. But the issue seems to be the 3.3V output signal coming from the Teensy 3.1. To fix this I need a level converter chip. I still had a 74HCT245 from another project laying around which works just fine :-D

Although this solution works just great. I eventually connected the strip to the Teensy 2.0 that I am using as my room automation hub, which has 5V output pins. I needed the Teensy 3.1 for another project and it is way more convenient to connect the LED strip to this Teensy instead of a separate one. Frees up another USB port on my computer, and I can now control it from my phone and tablet.