Linoleum will break down over time and split and crack. Then moisture can get trapped under it. And if you have several inches of bedding on the floor, you won't see it or notice it, until your foot goes through the floor.  Now it is a good idea to have something, if you have a wooden floor, over it to protect it. I used a rubberized roof coat product (Blackjack #57) that I got from Lowes. This stuff actually becomes a permanent part of the floor. It totally seals any and all floor gaps and joints. Also seals the floor to wall joint/gap. If it can stand up to all kinds of weather extremes on a roof, protecting a chicken coop floor is no problem to this stuff. To apply, just dump out on the floor (Stir well first) and push it around with a roller. After it drys, you won't have to worry about the floor again. 
Jack