As the question says on the tin: Can I integrate software under Creative Common for commercial gain? I want to use Creative Common software (e.g., http://thrivingkings.com/apprise/) for some big clients.
You are free to do so, provided you meet the requirements of the license.
In the case of Apprise, you are free to use it in any way you want, so long as you attribute the original author, and that you release any changes under the same license (CC-BY-SA 2.5). You are even free to use it commercially, since it doesn't have the non-commercial restriction.
Read the specific license and see if it is compatible with the sort of commercial gain you want to get. There are several Creative Commons licenses, and all sorts of ways to make money with software, some or all of which will not work with specific licenses. For example, you can't bring software under a GPL version into a proprietary product and distribute it, and you can't use something under a Creative Commons non-commercial license commercially.
My rule of thumb is that licenses mean what they say, and if you're careful to abide by the letter and spirit of the rules you should be safe. If you want to use the software in a way that's not definitely within the spirit, consult a lawyer. It will be a lot cheaper to get a quick consultation than it would be to get into legal trouble later. (If you're not going to use the software as the owner intended, why do you expect to do so without any legal costs?)
You can always ask the copyright holder for clarification or to see if you can use the software under another license. (There's a reasonably popular model where you can use software either under a Gnu GPL or pay money for a license that's less restrictive in some ways.) The worst they'll do is say "No", and then you're no worse off than before.