This is how I see it:
Chiang Kai-Shek continues to build up his central army and the authority of the government in Nanking. Assuming there is no provocations by Japan, Chiang eliminate the Communists entirely. If there are still diplomatic provocations, some form of United Front happens where the CCP survives, but it loses its basis as an independent armed force.
By 1940, Chiang has basically solidified control over most of southern and central China although some warlords retain a semblance of independence. He is collecting taxes in most provinces and has a 60+ German trained divisions and has begun the process of incorporating some of the provincial armies into his command or disbanding them. He has a modern air force and beginning to build a navy for coastal defense. The western and northern province warlords are still separate, but inclined to work more with him.
Chiang probably begins next in establishing central authority in the five northern provinces, probably under guise of preparations to finally deal with the Japanese in Manchuria. Perhaps under pretext of a military inspection, central army troops move into Shandong and Hebei to the Great Wall.
When France falls to the Nazis in 1940, Chiang probably begins aiding the Vietnamese nationalists, but does not take any direct moves against French Indochina. Allies can rest a lot easier that SE Asia remains calm during the war.
By 1942, Chiang has probably unified the country militarily and has around 100 divisions at the level of the german trained divisions. At this point Chiang likely begins making demands the Japanese leave Manchuria or face war. Or he might decide to take advantage of Stalin's preoccupation with the German invasion to assert his authority over Xinjiang and remove Sheng Shicai. It's even possible in exchange for Chinese friendship he gets Stalin to agree that Outer Mongolia is given back to China. If so, the crisis with Japan over Manchuria is pushed to 1943.
If the Japanese don't do anything in response to increasing Chinese power, a confrontation that will likely lead to war will happen in 1942/1943. Most likely, Japan sees the rise of China is a threat to their mainland empire and begins countermeasures in 1940 when Chiang begins to assert his authority in northern China. In any event, large probability a Sino-Japanese War erupts sometime between 1940-1943.
With the extra years of preparation, China does extremely well. Chiang likely holds onto both the Yangtze Delta and Canton, although it is possible minor ports along the Fujian coast are seized by Japanese marines to negligible effect. There are some terrible battles along the North China Plain, but China wins as many as it loses. While the Japanese soldiers are better on a one for one basis, there are just too many Chinese troops. After a year's worth of fighting, the Chinese are probably pushing into southern Manchuria.
Casualties are high, but after the Chinese take Mukden, the Japanese agree to some kind of peace in exchange for promises to recognize Japanese control over Korea and Taiwan and to return any Japanese property seized in China. Japanese investments in Manchuria are also probably protected although any strategic war industries become property of the Nanking government. The war probably lasts anywhere from 2-5 years depending on how late it starts.
In other parts of the world, FDR keeps increasing US involvement in WWII but avoids a declaration of war without German provocation. If the US doesn't enter the war, expect support for Lend Lease to the Soviet Union to decrease after 1943. As the Soviets begin to win, the US doesn't want them to win too big. That's OK because without the Japanese attack on Britain's eastern colonies, the British drive the Axis out of Africa in 1942 and invades Italy in 1943.
At this point, Allied strategy probably focuses on a combined Anglo-Soviet offensive in the Balkans timed with defections of Hitler's allies in 1944. This more or less succeeds, but manpower is running low on all sides at this time. A negotiated peace is not possible while Hitler is in power, but Churchill and Stalin might be willing to deal with a "moderate Nazi" government that ends the war in a clear win - reversing all of Germany's gains under Hitler, but leaving Germany itself unoccupied. How exactly the end game plays out is very debateable.
FDR does not run for reelection in 1944. Dewey or another Republican becomes US President.