How much time should you spend practicing? You'll receive a different answer from every musician you ask.
I believe that you should only practice for as long as you can maintain mental focus on what you are doing. For a beginner, this might mean 15 minutes at a time, or maybe even less. As you grow as a musician, your teacher will help you develop the practice techniques needed to work for longer periods of time.
In an ideal world, you would be able to practice every day of the week. With the exception of a conservatory setting, however, this is usually not a possibility. So you have to ask yourself how often and how much you are going to be able to practice during the week.
How many days of the week do you have time available for practice? The answer might be more than you think. I've found that planning out my week of practice in advance makes for a much more efficient use of my time. Here are two sheets I use (click the image for a downloadable version):
First, fill in a sheet with your normal week as you usually spend it. Include things like work, meals, downtime, and other activities. Afterward, take a look to see where things could be shuffled around to allow for adequate practice time and fill out another sheet with your revised schedule for the coming week.
The first sheet helps you lay out a game plan for the week, and the second one shows you how much time you intend to spend per day. Having a plan for the week can help avoid the "where do I even start" feeling that can sometimes lead us to skip a day when we could have otherwise made progress.
This being said, it's important to build an off-day into your schedule. Take one day per week off from practicing to allow your muscles to rest.
Your ability level is the biggest determining factor when figuring out how much time to spend playing your flute each day. Beginners need time to learn the proper playing position and breath control required to play for long periods of time, and as these skills develop, practice time can increase. Here's an outline of total daily practice amounts that I recommend for my students:
Beginner: 20-30 minutes
Intermediate: 45-60 minutes
Advanced: 1.5-2 hours
College Prep: 2-3 hours minimum
Whatever the amount of time you decide to work, you don't have to do it all at once. Dividing up your time into smaller chunks helps keep your mind fresh and helps you to retain the progress you've made. I like to split my practice time into two or three shorter sessions throughout the day. This helps stave off the mental check-out that can happen when you do the same activity for an extended period of time.
You get out of your practice what you put into it. Even if you aren't able to get in as much playing time in a week as you'd like, a shorter amount of creative, inquisitive practice is always more beneficial than hours of uninterested repetition. As Trevor Wye says, "It is almost useless to spend your allocated practice time wishing that you weren't practicing." Try giving yourself a structure to work within and see how it changes your practice.