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First, I'm an electronics noobie.  I've daisy chained 4 TLC5940s on a breadboard exactly as shown on the Arduino TLC5940 Library page and a total of 21 RGB LEDs.  One diversion from that setup is that I used a 2.2K resistors instead of 2K resistors (my local Radio Shack didn't have 2K resistors).

It works pretty well expect that sometimes one or two of the TLC5490s flickers it's LEDs. Any ideas?

Thanks! 
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How long are the connections between the tlc's?

Also, which tlc's are the ones flickering? The last two on the chain or is it random?
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I suspect you have no decoupling capacitors on the TLC5940s.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html
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How long are the connections between the tlc's?

Also, which tlc's are the ones flickering? The last two on the chain or is it random?

Four TLCs altogether.  Usually happens on the 2nd and or 3rd TLC.  Connections are about 3 inch jumpers. 
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I suspect you have no decoupling capacitors on the TLC5940s.
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.html

Thanks Mike.  I'm an electronics beginner so some of your tutorial was over my head but I think I got a rough understanding.  So the VCC and GRD on are pins 21 and 22 on the TLC5940NT.  Would I run a 0.1 µF capacitor between those two pins on each IC, correct?

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Quote
Would I run a 0.1 µF capacitor between those two pins on each IC, correct?
Yes that is correct.
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I have also the problem with random flickering for my 5940, and it happens on the first tlc already at OUT10 onwards. The first few output pins are ok though.

I have the 100nF between Vcc and GND. What else could be the problem? I'm using the Fades example code from the tlc5940 library.
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First, I'm an electronics noobie.  I've daisy chained 4 TLC5940s on a breadboard exactly as shown on the Arduino TLC5940 Library page and a total of 21 RGB LEDs.  One diversion from that setup is that I used a 2.2K resistors instead of 2K resistors (my local Radio Shack didn't have 2K resistors).

It works pretty well expect that sometimes one or two of the TLC5490s flickers it's LEDs. Any ideas?

It's 99% certain to be a decoupling problem. Lots of LEDs switching on simultaneously causes voltage drops on the logic parts.
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Continuing from my problem previously. I do have the decoupling 100nF capacitor on all my tlc's, and the problem still stands. Now I switched from a UNO board to a Nano 168 board and strangely the problem disappears. But the fading speed also becomes much slower. Again, I'm using the example Fades in the tlc5940 library.

So why the speed is different? Is it because of the faster clock speek on UNO? But I thought the example would have taken this into account when I change the board setting in the arduino menu.

And why the flickering disappears on the Nano but not the UNO?

thanks
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So why the speed is different? Is it because of the faster clock speek on UNO?

Probably.

But I thought the example would have taken this into account when I change the board setting in the arduino menu.

It's not guaranteed. There's plenty of ways to code a sketch that make it depend on a particular clock speed (in fact getting timing right is one of the most difficult parts of Arduino coding).

And why the flickering disappears on the Nano but not the UNO?

The clock/data signals to the TLCs will be running half as fast. Slow is more reliable for communication links.

I still say it's a decoupling problem. Where are you getting the 5V for the LEDs from? Try adding decoupling there.
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