China won't come to Russia's aid at the point of flashpoint and that is for many reasons which I will explain.
China has 2 front war and it will avoid openning both fronts at the same time and if East Europe flashpoint goes in flares it gives China opportunity to first solve one of the fronts. You may ask what two fronts China has? China's most lethal front is in it's eastern front which many don't talk about it. The US has 2 mechanized divisions on the DMZ and 5 mechanized divisions in Japan. That is 75.000 forces deployed there permanently and on the other side China has a front with India and as you can see China is first trying to solve this front before solving the other front because this is the easier front of the two fronts if Ukraine flashpoints opens China knows the Indian front becomes a viable option to solve in order to free itself up.
But if China was to rush to East Europe it will be flanked from the behind. It has nothing to worry about with India because Pakistan has them in check they won't flank but these 75.000 in the east will flank them from the behind if it were to rush to assist Russia in Ukraine or in East Europe hence it's hands are tied but China is unbothered by that because this opens up the opportunity to solve the gangu issue unaltered and it also has major allies in the region to do it with hence the operation would be much easier as it's Pak-Afg-central asia and Korean allies could deploy an additional 3-4m men for the campaign without including the chinese deployments. Hence if Russia were to fall on the west Then India will in return fall on the east. The US won't mind it tho to exchange Russia for India and will let it occur as it will guraantee China won't get involved but post that it will free up China
The only possible theological "flank" that can threaten China is from the North, Russia herself.
As you said, Pakistan keeps India in check. But it's not necessary, the Hymalaya already deny all possible attack from India
In the South, there is impenetrable jungle and mountains. Furthermore Myanmar ? no China have a few buffer zones there, Laos ? no way, VietNam ? no, we do not do that
In the East ? that's the sea and ocean. It's good for China if her enemies decide to try to land the force there.
Force projection over the sea is even more dangerous then the mountain, If the US - Japan - Korean , heck even the UN
want to try to land their forces in China using the sea, my bet is on China. The battle will be bloody and very quick.
When you look at the North: well, it's North China plain, then Beijing, then Central China plain all the way to ShangHai and HongKong. That's the reason why Japan invasion of China started in the north