If I buy an iPhone 14 in Singapore, will the warranty work in India?

In general, warranty service for iPhones and iPads is restricted to the country in which the device was purchased. That is what the US warranty informaiotn states:

As US policies do not apply to you, start here:

Legal - Hardware Warranties - Apple

Select your device type, then your country to see the terms that apply to you.

There is no international warranty; it may be available only in the country of pyrchase.