I want to design a board using Flex PCB. I can calculate the maximum current I can pass through a path on the PCB, but I couldn't find any documentation on how much current and voltage can pass through the flexible pcb. How can I learn this information?

 

Did you ask the people that make flex boards. Most have current calculators on the website.
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I would use the same numbers as for a rigged PCB using outside layers not inside layers.

 

Yes, I tried the calculators and applications such as saturnpcb on the manufacturer's sites, but I was not sure because I could not see a section about flex pcb.

 

Polyimide (amber color) Flex boards can handle the same or greater heat than an FR4 board. The cross-sectional area (copper thickness and trace width) determine current limit. Polyimide should have a CTI above 600v so anything up to 300v dc should be safe.

 

There are Printed-circuit-board (PCB) design textbooks and IPC standards do a good job of discussing a PCB trace's dc current-carrying capability up to about 30 A. However, little if any reference material exists beyond this threshold, either in current or frequency.

Good luck on 30A with a flex circuit. Flexibility tends to decrease a lot as thickness increases.