President Chiang Kai-shek instructed him to rebuild his former 13th army and defend his home province, Yunnan, from Communist attacks. By the time that Communist forces had taken the mainland in 1949, Li had already withdrawn his armies south and west, into Thailand and the Shan states of Northern Burma. When Burma declared independence in 1948, Li established an independent Shan regime for his "Anti-Communist National Salvation Army". From these bases, Li's units continued to carry out guerrilla attacks against the Communist authorities in Yunnan.[1]
Nationalist forces from Yunnan also attempted to move into French Indo-China, but these troops were quickly disarmed and arrested by the French. The troops which moved into Burma initially settled around Tachilek, in the state of Kengtung, near the Thai border. The troops who moved there under Li joined earlier Nationalist troops who had remained in the area after fighting the Japanese in World War II. Following Li's withdrawal to this region, Li reorganized all available Nationalist forces in the region, placing them under his command. Li's forces subsequently became known to foreign observers as the "93rd Division".[2]
What if the bulk of the Nationalist Chinese forces had followed General Li Mi to Burma? Say the Americans quietly get the French to allow them to evacuate there. Maybe his puppet(?) Shan regime plays host to them, and so do the newly independent Burmese or at least the Thai. With their presence, the VNQDD end up doing better and either the Vietnam War is averted and/or the Nationalist Chinese are involved in the civil war.
This would be an interesting situation because unlike Taiwan, there's no historical Chinese claim to the Shan areas of northern Burma, other than as tributaries. Probably not many Han there. (Edit - Wait maybe I'm wrong and their presence in the Shan states could be diplomatically fractious!) So this wouldn't be much like the ROC on Taiwan at all, but rather like the White Russian model. This could be bad for their aspirations because without a territory under their control that they could claim to be a part of China, they don't even have the Southern Ming exile model to have pretensions of being a legitimate government. Unlike Koxinga, they'd be more like the Black Flag Army, playing bandit. Though paradoxically, if they're able to find themselves a host and patrons (and based on Wikipedia, Burma and Thailand were receptive to some of the KMT generals because they provided training and advisory roles to their newly-formed militaries), they might end up being more active than the ROC- as a bandit army, they could run around SE Asia knocking off local communist movements and thwarting the external ambitions (if any) of the PRC. The KMT would receive a lot of covert CIA (and DGSE?) funding and end up being even more shady than OTL.
Also see: https://en.wikipedia.org/wiki/Santikhiri
Bonus points if you can rope in Hainan somehow.