Mess kits can be anything from a coffee can used for boiling water, to a 6-piece titanium micro-kitchen. Your mess kit needs only to meet your needs for preparing food and water.
When choosing a mess kit you will need to consider weight, size, durability, materials used and most importantly what you want to prepare with it.
Obviously weight is of great importance to a bug-out bag, the primary factors that determine the weight of your kit will be the material and number of items. Titanium is lightweight, durable and doesn't leach into the food, but is generally expensive. Stainless steel is heavy, durable, doesn't leach into food and cheap. Aluminum is lightweight, durable (too a lesser extant than steel), and is reasonably price; some research has shown that aluminum might leach into food and cause health problems, but this is inconclusive. Finally, you should consider what items you actually need to have, if you only need to boil water then a small pot will suffice, if you wish to be able to cook like you can in a full kitchen then you may have to get used to carrying significantly more weight.
Mess Kit Items
There are many different items to cook with, and they could all be part of one's mess kit. Using good judgment in choosing which of these items you will carry will help you save weight and space in your Bug-out bag.
The pot or "billy can" is the most versatile of mess kit items. It can boil water and food, stir fry, bake, etc...
Frying pans are convenient because pan-frying is quick, easy and yields good flavor, but it will cause you to lose some nutrition. Most quality frying pans also tend to be very heavy.
Kettles are convenient for boiling water, as they will generally bring it to temperature faster than an open pot, and also make pouring easier. If they are properly shaped and large enough, they can replace a pot.
Metals cups can be used as a small pot for boiling water or preparing a small amount of food.
Plates and Bowls
While not strictly necessary, a plate or bowl allows you to remove food from a hot pan or pot to eat it.
Eating utensils make the consumption of food easier and cleaner.