If I flip a blue hybrid battle icon, does it become an orange hybrid battle icon with the same trait?
[Source: WotC]
Yes.
Belligerence would turn this flip of normally [OU, (OUB)] to [OO, (OOB)], meaning that you only flipped 2 colors on defense--Orange and Black, regardless of your character’s tratis--and would thus get +2 DEF for that battle.
No, it would be unable to trigger cause your oranges would be blues so your attack will not meet the flipped icons requirement. Note: Your own Belligerence would also cause the ability to fail.