No, check Ryujin's post above.
A Radiant Smite with a Flaming Weapon (activated) deals radiant AND fire damage.
That doesn't make any sense.
Flaming weapon states:
Power (at will - fire)
Free action. All damage dealt by this weapon is fire damage. Another free action returns the damage to normal.
In what way does the above say that all damage dealt by the weapon is fire damage in addition to its previous damage? I don't think the power could be written any clearer "All damage dealt by this weapon is fire damage". Surely that tells you everything you need to know?