Chiang lacked the charisma, political astuteness and legitimacy to maintain a unified China. Chiang basically took over the KMT because he had all the guns in the KMT.
Most original followers of Sun looked down on what they considered a mere hit man. To them, CKS was no different than other warlords, such as Li Zhongren, or Zhang Zoulin. Not to mention CKS had a very corrupt inner circle, many of whom were within his family. CKS was in constant battle with the non-military KMT types, and whenever he failed, those old guards would push him out of power.
If CKS did win the civil war, he would have gained more esteem. I imagine he would be even less willing to let go of power, seeing how he wouldn’t let go of power when he failed in the real time line. (While he did step down after the CCP had crossed the Yangtze, he maintained real control over most of the armies and refused to cooperate with the acting president Li Zhongren.)
CKS would start a purge within the party to rid KMT of the old guards (actual Sun followers, many of which were pro-communism to begin with). CKS also would need to force complete capitulation from other warlords within the KMT, such as Li Zhongren, and Zhang Xueliang. Those forces would unite and turn against CKS sometime in the late 1950s. The KMT old guards and dissatisfied warlords would point out the corrupt and dictatorial actions of CKS and rally up enough public support to have enough forces to put on a couple of major battles.
Most in the US would be very annoyed by CKS, and his dictatorial rule, but they needed CKS and China to act as a buffer between the Soviet and the rest of Asia. However, they probably would refrain from giving either side too much support.
The Soviets would seize the opportunity and reorganize the communists, but since Zhang Xueliang still had control over Manchuria, they would have achieved very little.
Mongolia (both inner and outer this time), Tibet and East Turkistan would however use the opportunity to gain full independence. Taiwan would follow the trend, since in the real timeline, Taiwan experienced the 228 massacre before CKS lost China, so in this alternate timeline, with the support of former Japanese officers, Taiwan would declare independence while pointing out KMT unlawfully incorporated Taiwan as a province of China.
I imagine the outcome of the civil war would be a fractured China, with Chiang holding the South East coastal areas. Zhang Xueliang holding most of the North, and Li Zhongren controlling Guangxi and most of the central parts of China.
The US would support all 3 to continue acting as buffers. Korean war would be avoided. Ho Chiming would still carve up half of Vietnam, but would be less effective and wouldn’t take over the whole thing.
All in all, China and Asia would still be a mess, but the end result would be less dead people, especially less starved people, and a much stronger US.