How is one reborn as a chakravartin?

DN 26 states Cakkavatti was achieved as follows:

He had over a thousand sons who were valiant and heroic, crushing the armies of his enemies. After conquering this land girt by sea, he reigned by Dhamma, without rod or sword.

More brief reasons for this 'rebirth' or 'becoming' can be read in AN 3.14.

Chakra-vartin ("wheel-turner") is, by definition, a ruler that turns the wheel of Dharma. The wheel of Dharma is a metaphor for tradition of wisdom and virtue, passed from generation to generation. As the wheel keeps going in the established rut, an established tradition keeps getting passed from generation to generation of people.

So the chakra-vartin is an epithet of an ideal ruler that preserves and maintains the tradition of wisdom and virtue as the mainstream principle and paradigm during the time of his rule.

As described in DN26, the way a ruler becomes a chakra-vartin is by

• upholding the primacy of law
• providing justice and security to all people
• protecting the animals
• supporting the poor
• consulting with the sages on questions of ethics

The key requirement seems to be consulting with the sages vs. ruling according to one's own ideas. In other words, to become a chakravartin one needs to educate oneself on ethics and consistently implement those principles in one's rule.

Generally speaking, over many lifetimes, it is "doing what's skillful" is what culminates as rebirth of a chakravartin.

Just double checking, you asked how one is reborn to... right? now how one accomplish such task?

In Sankharupapatti sutta, though it does not say exactly "cakkavattin", Buddha talked about causes for one to become whatever he/she wish: from human world, heavenly worlds, all the way to liberation. If he poses/accomplishes in

• faith (saddhā),
• virtue (sīla),
• learning (suta),
• charity (cāga),
• wisdom (paññā).

Interestingly, if you look at 5 qualities above, it is above quality of a stream enterer.

I think that what is taught to children about a "universal monarch" -- together with The Legendary Account of the Four Sights, in the Introduction to the Jâtaka -- is that the prince Siddhattha might have been one (and that his father wanted him to become a ruler), and that he chose not to be:

Seven of these raised two fingers each, and gave a double interpretation, saying, "If a man possessing such marks and characteristics continue in the household life, he becomes a Universal Monarch; if he retire from the world, he becomes a Buddha." And then they set forth all the glory of a Universal Monarch.

But the youngest of them all, a youth whose clan-name was Kondañña, after examining the splendid set of marks and characteristics on the person of the Future Buddha, raised only one finger, and gave but a single interpretation, saying, "There is here naught to make him stay in the household life. He will most undoubtedly become a Buddha, and remove the veil of ignorance and folly from the world." For this Kondañña was one who had made an earnest wish under former Buddhas, and was now in his last existence. Therefore it was that he outstripped the other seven in knowledge, and saw but one future; inasmuch as a person possessed of such marks and characteristics would never stay in the household life, but would undoubtedly become a Buddha. So he raised only one finger, and gave that interpretation.

So at least one of the requirements for that "achievement" is to "stay in the household life".

Wikipedia says,

The first references to a Chakravala Chakravartin appear in monuments from the time of the Maurya Empire (322–185 BCE), dedicated to Chandragupta Maurya and his grandson Ashoka. In Buddhism, the Chakravarti came to be considered the secular counterpart of a Buddha.

I guess that the conceit (of comparing "universal monarch" and "Buddha") might have been consolation and/or flattery for the emperor, or perhaps just good advice for the emperor.

The biographies (including birth, achievements, etc.) of Chandragupta Maurya and of Ashoka are also linked on Wikipedia -- see especially Conquest of Kalinga & Buddhist conversion but also Buddhist kingship.