malloc in kernel
Note about the difference between the two allocation methods - kmalloc and kmem_cache, or vmalloc:
kmalloc: Best used for fast allocations that are smaller than a page (PAGE_SIZE, 0x1000 on most architectures). It doesn't involve mapping memory, so you get the memory straight from the kernel's 1:1 physical memory mapping. You get physically contingent memory. Note that if you you want to allocate more than one page (i.e. order > 0), you risk bumping into external fragmentation issues - i.e. the call might fail even if there is enough free. Higher order - higher chance for allocation failure, and up-time plays a factor here too.
If you want to achieve maximal allocation efficiency then using your own kmem_cache for each type of struct is the way to go (the other benefits for this strategy are being able to monitor the state of your allocations from /proc and catching memory leaks more easily).
vmalloc: Allocations of more than one page. You get mapped-memory in kernel space. Behind the scenes it is similar to what userspace gets - the kernel allocates a bunch of pages and maps them in a virtual address space. This allocation is slower than kmalloc's, and memory accesses might incur a bit more overhead.
You can't use libraries in the kernel. None whatsoever.
This means that ANY function you're calling in the kernel needs to be defined in the kernel. Linux does not define a malloc, hence you can't use it.
There is a memory allocator and a family of memory allocation functions. Read the kernel docs on the memory allocator for more information.
Incidentially, there are a few functions the kernel defines which are in the standard C library as well; this is for convenience.
It does, for instance, defined snprintf