Out of all the general band instruments, the flute certainly sounds the most angel-like, and adds beauty to any arrangement. But what happens when you don't have the beautiful wavering of vibrato at the end of your tones? Vibrato is certainly not necessary, but it can improve your tone and overall beauty of playing.
Pick a note that is generally very easy to play, such as a b-flat or a D. Take a deep breath, and start your note. With your breath, make a little "bump" in the sound by letting more air through for just a moment before going back to your normal air stream. The note should get louder during the bump. Practice this technique––it should be easy. The bump/breath should come from your belly and diaphragm. If you are a singer, you know how important it is to use your whole stomach and lungs to get good air. You may need to tense your core a bit to control your sound.
Start a metronome on a moderate tempo in 4/4. You can also just keep basic time in your head or by tapping your foot. Make a bump in the sound on every beat for several measures. Slowly, increase the speed of your beat/metronome. It will take some time to get it right, but don't worry, with practice it will sound better as you practice more.
Keep increasing your beat until it sounds more like a full vibrato. It is extremely important to use your core and air to stay steady and even with your beats. This is why you shouldn't jump to faster tempos before you've gotten the slower ones down-pat. Also keep dynamics in time. Focus on your sound, and make sure the dynamics are generally even on each beat. src="//cdn.shopify.com/s/files/1/1156/2184/files/Screen_Shot_2017-08-21_at_9.57.33_AM_large.png?v=1503327472" alt="" />
Practice until you can do a generally moderate vibrato with an even tone. If you're confident, try seeing how long you can go for. If your tone is bad, it doesn't count, so make sure your tone is doing well. After a few exercises, you may choose to practice increasing the tempo even more.
Integrate the vibrato into a piece of music. Don't start with fast pieces; you need to take it slowly to begin with. Start with a sonata or something similar. You will need to rely on your personal opinion on what notes should have vibrato. Long notes usually do, and some people do it with every note, even in fast pieces like marches. Using vibrato in pieces can be much harder, but it is easy to get the hang of once you've done it well.
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Slowly increase your speed or move to faster/more complicated pieces. By now, you are a vibrato expert! Make sure you aren't hard on yourself if you don't get the hang of it immediately. These skills take time.