ChineseDateFormat has not been ported to icu4c, but the functionality it provides (adding a symbol in the case of the current month being a leap month) should. The best solution may be to remove ChineseDateFormat from icu4j and modify a general DateFormat in both icu4j and icu4c directly.
If that is the best solution, it should probably be done after ticket #6033, where it's pointed out that IS_LEAP_MONTH is in different places and that the one in icu4j should be moved.
This is also related to CldrBug:1507 , where <isLeapMonth>, <leapSymbol> and <nonLeapSymbol> are proposed additions to CLDR specs. However, the data is already in the icu supplemental CLDR data (root.xml) waiting to be used (and I believe it's already in use by ChineseDateFormat).