This is kamailio forum and as you mentioned all is working on kamailio side. Any standard SIP client should work with kamailio without any problem, regardless if its a mobile app or desktop softphone or even an ATA.

Regarding SIP client SDK for mobile apps, there are several available, both commercial and opensource. A few examples below,

http://www.pjsip.org/
http://doubango.org/
http://plivo.com/voip-sdk/
http://www.acrobits.cz/27/acrobits-mobile-voip-solutions
http://www.linphone.org/eng/documentation/dev/liblinphone-free-sip-voip-sdk.html

Thank you.