So basically i use Flame Arrows on one turn as a bonus action and do a regular attack with my bow. 

Next turn i do Conjure Barrage which makes the targets do a dex save or take 3d8 damage on a failed save, does the flame arrows add an extra d6 fire damage to the 3d8?

Conjure Barrage would be using the same ammunition that Flame Arrows affected 

I don't think so.  Conjure Barrage requires a nonmagical weapon or ammunition, but the ammunition affected by Flame Arrows would be considered magical, so they could not be combined.

The spell Flame Arrow cannot benefit a Conjure Barrage  because it also isn't an attack that hit using the ammunition but saving throw instead.

Okay, but what if you were to just set a mundane arrow on fire and then cast conjure Barrage? Would you still just have them deal piercing damage, change it completely to fire damage, or go 50/50 fire/piercing damage?

That would be up to the DM if they would allow Conjure Barrage to work differently with arrows that are on fire, but RAW it'd still be piercing.