You can take a look here: https://github.com/Sarcasm/irony-mode#i-got-an-error-due-to-stdargh-how-to-solve-this
The variable irony-libclang-additional-flags
should meet your needs.
It should work without calling irony-reload-flags
.
It's not a buffer-local variable though, so you don't need to put it in the hook.
I would recommend the following:
(setq irony-libclang-additional-flags
(append '("-I" "inc") irony-libclang-additional-flags))