It seems there’s a real temptation to begin a new, unfamiliar piece of music, and then attempt to play it through, from start to finish, in tune and on time, and it also appears that there are those rare players who can do just that, but then there are the rest of us, myself included, who must work at it.
So, what to do?
Well, one proven technique is to break a new piece of music into many little pieces, as bite sized chunks, of maybe two measures. Work on the first two measures until they are comfortable, then work on the next two measures until they are comfortable, and then try putting them together, to make a sequence of four comfortable measures. Then, in a similar way, keep adding two more measures at a time. Eventually, you’ll have a “string” of measures, and a complete piece of music!
Now, when it comes to the flow of the music, wind instruments (pipes excepted) are at a natural disadvantage, simply because a player must momentarily stop, to breathe. Here, however, the general rule is to not breathe on the beat, as it’s the beat which keeps the flow going! So, try breathing either just before, or just after, the beat, depending on circumstances. It can also be helpful to breathe more frequently, to take smaller, shallower breaths more often, at least until you know a piece so well that you know just how often you must breathe. A shallow breath simply takes less time than a deep breath, and, as it happens, in the world of flute playing there are some relatively long, technical passages which simply demand a frequent series of quick, shallow breaths, in order for the flow of the music to remain alive.
Edited, a little 