Instead of writing a flat sign before every Bb note, it is easier to write just one flat sign after the treble clef. This means that all B notes on the staff are played as Bb even though there is no flat sign placed before the note. This is called a key signature. See Lesson 9 for more information on key signatures.
Play all B notes as Bb as indicated by the key signature. Notice that there are no breath marks in this example. Since there are plenty of rests, you can take a breath any time you see a rest. Breathing where rests occur is a good general principle in all wind instrument playing.
Sometimes it takes only two or three notes to create a good flute part for a song. In a song like this, where and how the notes are played is the most important thing.