Is there a Chinese-Chinese dictionary api or database available that I can use in my own app?
I think you might get this kind of database from some publication press if you are lucky, but it seems to be not an easy way. 

Also, I didn't find any database or flat text with Open Source License from the Internet.

But here is a website which is quite clean and neat. http://www.zdic.net/

I tried to look up a single Chinese character(字), and the request link seems quite tidy. I tried 好 and it showed http://www.zdic.net/z/17/js/597D.htm ,where 597D is exactly the UTF-8 code of 好. So you may use this as a breaking point to implement your dictionary function. 

Also, if your app is for commercial purpose, please don't forget reading the license of this website before using it ;) 

Have fun coding!