My kohler 12res starts but governor moves constantly which makes my voltage erratic

question to you
are the rpms erratic under no load ( is the engine hunting on the governor)
at what load setting does the problem start to occur

Try a static governor adjustment first as it simply be out adjustment.

Static Adjustment Procedure
Make this adjustment whenever governor arm is
loosened or removed from cross shaft. Adjust as follows:
1. Make sure throttle linkage is connected to governor
arm and throttle lever on carburetor.
2. Loosen nut holding governor lever to cross shaft.
3. Move governor lever toward carburetor as far as it
will go (wide open throttle) and hold in this position.
4. Insert a long thin rod or tool into hole on cross shaft
and rotate shaft clockwise (viewed from end) as far
as it will turn, then torque nut to 6.8 N·m (60 in. lb.).

Try doing a static governor adjustment.

Static Adjustment Procedure
Make this adjustment whenever governor arm is
loosened or removed from cross shaft. Adjust as follows:
1. Make sure throttle linkage is connected to governor
arm and throttle lever on carburetor.
2. Loosen nut holding governor lever to cross shaft.
3. Move governor lever toward carburetor as far as it
will go (wide open throttle) and hold in this position.
4. Insert a long thin rod or tool into hole on cross shaft
and rotate shaft clockwise (viewed from end) as far
as it will turn, then torque nut to 6.8 N·m (60 in. lb.).

It could be a number of things bad regulator, bad ground, wiring

SCFO is either what is displayed just before it cranks or when it is first powered up. Sounds like the controller may have forgotten what engine its running or is getting a bad run signal from the start switch. In either case a 1 year old controller should not be doing this. I would try having a local dealer doing a firmware update as there were quite a few for this controller and if this doesn't fix the problem I would start talking warranty with whoever replaced the controller.

If it has a couple hundred hours or more, try cleaning the slips rings on the back of the rotor shaft. They should be very shiny and not black or polished looking.

Lowes sells air filters for Kohler engines . As far as the oil a SEA 30 or 10w 30 would be fine.

Sounds like a short in one of the windings to me. Can you verify that the engine rpm is not exceeding specs? If you can modify the engine speed Id say slow it down and see what the voltage read is.

Here is the code explained direct from Kohler's manual. I'd disconnect the generator load first.
UU Undervoltage Shutdown occurs if the voltage falls below 80% of the nominal system voltage for more than seconds. Check wiring and connections.
Reduce the load and restart the generator set. —
Check wiring and Check controller configuration, system voltage
and frequency (parameter UU).

Check AC voltage and adjust, if necessary. 5.7
Replace the SCR module and test voltage again. 4.9
Separately excite unit. 5.2
Check stator continuity

See web site for manual :http://www.kohlerpower.com/onlinecatalog/pdf/tp6196.pdf

check connections on speedsensor or take down rpms must be a screw or bolt on de fuelpump