Currently, it seems all the Vulkan tutorials and samples use NativeActivity on Android platform. I would like to know whether we can use Vulkan with Java Activity on Android?
Yes, you can use Vulkan with your own Activity subclass. Because Android doesn't have Java-language bindings for Vulkan, you'll need to use either JNI or a third-party Java Vulkan library (which is just doing the JNI for you).
Your View hierarchy will need to contain a SurfaceView, and when you get the Surfaceholder.Callback#surfaceChanged callback you can get the Surface. If you're doing the JNI yourself, you can call ANativeWindow_fromSurface to get the ANativeWindow from the Surface, and use that to create your VkSurfaceKHR/VkSwapchainKHR.
The one thing to be careful of is to avoid blocking the main UI thread when calling VkAcquireNextImageKHR. Either arrange so that you only call that when it won't block for long, or put your frame loop on a separate thread.