Breathing is a very important part of singing. A fun way to have kids exercise their breathing is having them pretend to be a dog. Panting like a dog stimulates the diaphragm which helps develop vibrato. Have them start with a slow pant and gradually increase it to a pace where they are panting as fast as they can. They will probably be laughing by the end of it.
This is a common exercise that doesn't feel like an exercise. A tongue trill is done by placing the tip of your tongue on the roof of your mouth, breathing out and producing sound at the same time. A lip trill is done by placing your lips lightly together, breathing out and producing sound so that your lips flutter. You can make any sound or use scales to warm up.
Most kids know the vowel sounds, "A," "E," "I," "O," and "U." A fun exercise is to have them sing the vowels. First have them say the vowels as if they were speaking. Next, have them open their mouth in a relaxed position and have them try and make the vowel sounds without moving their lips and jaw. You can have them practice the vowels sounds while doing a scale. You can also have each child do one vowel sound and then switch until they've all done each sound.
Scales are excellent exercises for any singer or musician. An exercise that can be fun for kids involves using a different consonant in front of a vowel sound while doing a scale. For example, making a "Mmee Mmee Mmee Mmee Mmee," "Mmoo Mmoo Mmoo Mmoo Mmoo," "Mmay Mmay Mmay Mmay Mmay" sound for each note of a scale. Change the consonant. "Laaaa Laaa Laaa Laaa Laaa," "Looo Looo Looo Looo Looo," etc.
Singing songs is the goal of any singer. Have the kids sing parts of a song. Give one child a verse, another child the chorus, another child the bridge and then have them sing the entire song together.