I have a multi boot set up with two Linux distributions and Windows. If I upgrade the kernel of one Linux distribution would it cause breakdown in grub boot selector for selecting which operating system I wish to boot? If this is right is there any solution for this?

Upgrading the kernel could break the grub loader for that OS, and, in limited circumstances, for another Linux OS in a multi-boot set up, but only if a set of conditions existed, those being:

• That the kernel upgrade removed the old kernel and changed the name of the kernel image in /boot
• That the kernel upgrade over-writes a kernel belonging to a different OS

Personally, whilst I have seen the first, a simple sudo update-grub would fix it. I have never seen the second. If you are multi-booting including Windows, your Windows boot entry shouldn't be affected at all.

A fix should be relatively easy, by booting a live CD, chroot into the OS owning grub and sudo update-grub. Alternatively, you could boot a live CD, mount /boot and manually fix /boot/grub/grub.cfg

Very unlikely.
Note that update-grub is not part of the grub[2] package, but likely will be available on Debian derived systems (certainly Ubuntu).

Personally, I use burg, which tends to mirror grub, and I've noticed that update-burg is no longer provided, but burg-mkconfig is. I assume that similar is available for grub.

Having said that, I've been maintaining burg.cfg (grub.cfg) manually for so long that I lose track.

Depends on how you updated the grub It could breakdown the grub if not done in the right way. Preferably use the tools that are available with the distro.