Is the plane legal to fly?

Start with 91.205

14 CFR 91.205 lists the equipment required for VFR flight. Day VFR is the TOMATO FLAMES list, and night VFR adds FLAPS: fuses, a landing light (if flying for hire), anticollision lights, position lights and a source of electrical power. Flaps aren't on either list. But 91.205 isn't the only rule that applies, so it can't answer the question by itself.

Then 91.213(d)

Most Part 91 trainers don't have a minimum equipment list (MEL). Without one, 91.213(d) lets you fly with inoperative equipment only if it isn't:

• part of the VFR-day equipment required by the airplane's type certification
• listed as required on the airplane's equipment list, or on the Kinds of Operations Equipment List (KOEL) for the kind of flight you're making
• required by 91.205 or another Part 91 rule for that kind of flight
• required to work by an airworthiness directive

If it passes those tests, the inop equipment has to be removed or deactivated and placarded "Inoperative", and a pilot or mechanic has to determine that it isn't a hazard. On newer POHs, the KOEL is in Section 2. Whether inop flaps pass depends on the airplane, which is why the answer is to check the FARs and the airplane's documents.

NOTE: This is not to say you should fly it. As a matter of fact, just because something is legal, doesn't mean it's right. The point is there's more to consider than just 91.205 when preflighting.

Who decides

The FBO can tell you about its airplane, and as a renter you should ask. But the pilot in command decides whether the airplane is airworthy (91.7), and the answer comes from 91.213 and the airplane's documents.

Are flaps a flight control?

Some CFIs and mechanics argue that flaps are a flight control, so an airplane with inop flaps is unairworthy. There's no clear FAA interpretation on it. A flap that's disconnected or free-floating is a maintenance problem, not a 91.213 deferral. Either way, the place to start is the FARs and the airplane's documents.