I have a developed a board game AI in C++. The game file consists of several header and sources files which I want to import to UE4 . Is it possible to use our own objects for integration with UE4?
If yes, can I develop my game for both PC and android platforms?
If it is normal C++11 compatible code, just start a new C++ project and add your source code as is. I did so with other C++ libraries and it works like a charm. You can use all what C11++ has to offer but you might run into some platform dependent issues with your native code when bridging the gap between your code and unreal code like String handling etc. Did not happen to me as I only use non-string libraries so be aware of that.
Best is to learn the way C++ is meant to be used when developing a Unreal game and incooperate your chess engine and test it on all your target platforms. For a chess engine it should be painless transition especially since you wrote the chess engine yourself, you will be able to debug upcoming problems easily. If you run into problems you can ask specific questions here in the forum and elsewhere (like discord/reddit)
PS: You can develop an Android game this way as well.