It is normal for Persians to have brown eye discharge. Whites are the hardest of all Persians to keep clean because they stain so easily, so you can expect to have to clean her eyes probably 2 x a day to keep them free of tears. I have a 10 wk old white kitten that I am currently getting into show condition and what I use on him is Eye Envy. It is the best product for reducing and lightening stains. You need to buy the original solution that contains an antibiotic in it (it needs to be refrigerated), and the lightening powder to apply after you have wiped the eyes. The powder is important because it lightens the stains that are already there and protects the fur from getting restained. You can use a cotton makeup remover pad (like Swissors) to wipe the eyes and a Q-Tip to apply the powder. Eye Envy sells a starter kit that you may want to get and full instructions are included, but don't expect the stains to go away overnight. It looks like your kitten has food or milk stains on her face. The only other way to get rid of these stains is the remove the stained fur. You can do that with grooming tool called a "stripping knife". They sell them in the Petsmart dog grooming section. This tool gently stripes off the top layer of fur and since fur on the face grows back the fastest, within a month or maybe two, your kitten will have new unstained hair. If you do this, I would still get the Eye Envy though, because you are going to need it. You can also ask your vet to prescribe you an antibiotic eye drop like tobramycin or gentamicin. Put the drops in her eyes 2 x day for 10 days and her tears will run clear for several weeks. Managing the tearing on a white cat is an ongoing process that you can expect to do every day for the rest of her life.
http://www.eyeenvy.com/Search.bok?category=All+Products+for+Cats
You will also need to bathe her. I bathe and degrease my pets once a month. Kittens can be degreased just like adults.
Here is my boy Mikimoto:

Thank you for all the info. I went looking for tear stain remover today and after looking I will be ordering the eye envy. I'm so excited to try it. As for the stripping knife... That sounds scarey for me to use! I'm nervouse enough at the thought of giving Dutchess her first bath as it is!

BTW how many cats do you have?

I have 9. It was an accident. Really, it was. Seriously, I never meant to have more than 4, but my vet gave me one or two who needed specialized diets or be put down, I rescued 2 Persians from starvation and euthanasia at shelters, and my husband totally failed at fostering one Persian. (Then there's hubby's 2 d-o-g's, but they're a whole other problem.) The saving graces are no kids, most are very healthy, and my vet, since she helped getting me into this mess, gives me a group discount!