What you require is commonly known as filters. Basically within a mobile app, there are a number of filters we can incorporate using base Android/iOS classes and adding a few others. Each of these create a photo effect without destroying the base photo (non-destructive editing).
This is not easy and unless your programmers have experience with this, you may want to sub-contract this to an agency that has.
I taught a class on this at Adobe MAX in previous years using the standard Adobe AIR mobile tookkit. The end app could apply 8 basic filters. I would not recommend using Flex or AIR to cross compile for many platforms and would recommend using native app code instead. The end result is a faster app and a smaller footprint that will run on more devices.
I had started porting some of this to native. To begin with, it would be good to understand what filters or effects you have in mind. The basic ones would be able to do black and white conversions, gaussian blurs, etc.
This site would be good to explore. https://pixlr.com/o-matic/
After that, a consultation would be best to figure out how to proceed.
The libraries used above can provide you with these effects but if you want truly unique filters, you may want to create your own. This requires someone with a lot of mathematic and graphics knowledge.
Good luck. Ping me if you need help.