My first guess was running package manager checksum verify, like "rpm -V kernel" , for rpm based distro. But i'm not sure if it was the question was aiming for.
The question, as written, has no answer. fsck only checks the filesystem. There is no way to check the consistency of the running kernel but a kernel panic is a telltale sign of INconsistency :)
You can check the consistency of the kernel "file" and compare a MD5 / SHA-1 of known good kernel. Assumption here that the kernel is loaded into healthy hardware. Depends on the spirit of the question. I do agree, running kernel looking at itself... chicken::egg.
I was very confused on this question as well. Seeing both kernel and filesystem there together with the word consistent made me think of a sort of general health. So my answer would have been `iostat`. That would show me the running kernel, cpu utilization, and disk utilization.
I presume 'not much' or 'you get an error', but I don't have an instance I'm prepared to sacrifice right now, just in case something hilariously destructive happens.
fsck doesn't run on a directory, it runs on a block device. You can't run it on /proc or /sys because those aren't backed by a block device. /proc only looks like it has a file system because the kernel "pulls" the "files" out of thin air when you try to access them.