Yes it's normal for burns to peel.
As the burn heals the skin starts peeling off to replace itself with new skin so it's a good thing if your skin is peeling as the burn is healing.
Severe burns need surgery to replace skin that was taken off through either a donor for skin or yourself from another part of your body.
But for smaller less severe burns the skin should eventually heal itself and new skin should grow over the old burned skin.
Just like when you get a sunburn the old skin peels off to make way for new skin which is normal and it's a good thing when sunburned skin is peeling off.
Although you should protect yourself from sunburns as well because sunburns can eventually sometimes lead to skin cancer.