Each conductive thread has a different spec so I am not sure what the exact current rating each thread. However, this is what I found from my tests that might be of some use for those that are using conductive thread:
Maximum Current with Conductive Thread?
Keep in mind that the stainless steel thread is like a really thin copper wire so there is a certain amount of power that can be applied through the thread. It would be safer to test the conductive thread with a multimeter placed between the power supply/battery and the system to determine the amount of power that is being pulled. Stress testing one small thread with a benchtop power supply and shorting it, I noticed that it would get warm at around 500mA at 4.2V. Between 500mA-1A, the thread started to glow red. The best is to use the conductive thread with the LEDs pulling less than about 240mA-380mA just to be safe.
When using a 1000mAh LiPo battery with 25 LilyPad LEDs in parallel (with current limiting resistors) there was about 82.5mA. Doubling the thread up and having more conductive material can help but you would still want less than about 240mA-380mA. We do have a specialized small battery that limits power for e-textile projects https://www.sparkfun.com/products/13112.
Otherwise, soldering stranded wire and securing the terminals (hot glue, designing boards with strain relief, or tying the wires down) might be better if you require higher power applications. An example is the 12V LED strips that I used for one my projects. The amount of power is a lot more than the conductive thread could handle.
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