How do I calculate what a successful reflex DC save when trying to dodge against the flaming sphere?
The DC for a saving throw against a spell is 10 + the spell level + the caster's casting stat modifier + any other bonuses, such as the spell focus feat . This is stated in the class descriptions of each class that can cast spells. Flaming Sphere is no exception and I can't see why you'd think it would be.
For example, if the spell was cast by a Wizard with 18 Int, the DC would be 16 (10 base + 2 level + 4 int).