I read that slight rib flare can be from improper breathing (not pulling the ribcage back in when exhaling). Can core strengthening help correct this?

Mgt. This may indicate a muscular or neurologic problem causing weakness of the chest wall. There are exercises to improve your chest wall strength, but I would recommend seeing your PCP. They can order some pulmonary testing including MIP/MEP . A virtual appointment can be booked online, to review once the results are available.