JNI and Java: ant calling make or make calling ant?
As a simpler alternative to JNI, try JNA: https://jna.dev.java.net/, may solve this hassle for you and be simpler (assuming it can do what you want).
I strongly dislike make because of its implicit ruleset and treatment of whitespace. Personally I would use cpp tasks (http://ant-contrib.sourceforge.net/cpptasks/index.html) to do my C compilation. They are not as flexible as make but they are also far less complex and it will mean you don't have to burden your developers with learning make.