I have one resource group where test, UAT and Prod instance of the application is hosted. Is it OK to create 3 Azure Key vault in the same resource group where these 3 instances (test, UAT and Prod) of the application hosted?
Is there any Microsoft official documentation on this?
It is certainly possible to do so. There is no restriction from Azure that would prevent you from creating resources of same type in same resource group. Your KeyVault name must be globally unique though.
However, as mentioned in the comments, it is advisable to keep your resources in separate resource groups by environments (or some other criteria) for better manageability.