There are lots of things within the Krypt in Mortal Kombat 11. Flaming chests are just one of the many mysteries you'll come across. Hell, if you're playing on the Switch then you're going to be more confused by the lack of scenery than anything else.
The first thing you need to do in order to quell these raging flames it to grab the Spear of Hanzo Hasahi (Scorpion's Spear) you can do this by following this handy little guide. Aren't we good to you?
Once you've done this you'll need to actually find one of the flaming chests within the Krypt. This is easier said than done due to the way the Krypt populates itself with items and collectables, but at least they stand out.
Having located one of these chests you need to first put it out. You can do this by having a look around for a hanging fire pot lantern. More often than not you can find these near the chests, but they can be anywhere in the area so it can take some time to find it. Once you have, use the Spear to hit the lantern and the fire on the chest will be put out. *note: this is not how you fight fires in the real world.
Once you have quelled the chest's burning desire you can make your way back to it and open it up. Well, you can if you have enough Hearts to do so. Hearts can be earned as you explore the Krypt but are also awarded when doing fatalities in other modes. If it feels like a grind, that's probably because it is. You can only hope you get an item you actually want, and not some nonsense item related to Johnny Cage. Maybe a nice new hat for Raiden or a kitten for Sub-Zero to play with. Or a kitten for you to play with.