Generator tripping GFCI breakers in main panel
That's to be expected.  The neutral from the circuit is going through the GFCI breaker, but the hot is coming from the generator.  The GFCI sees this as an imbalance, since there's no current flowing through the hot side of the breaker.

Here's what your setup likely looks like (if it was drawn really quickly in MSPaint).

If you follow the current through from the generator, you'll see that it returns through the GFCI breaker.

However, since the current is not flowing through the &quot;hot&quot; side of the breaker.  The breaker sees an imbalance, and trips.

The cutaway in this image shows the internal circuitry of the GFCI breaker, and depicts the current flowing only on the neutral wire.



WARNING:
If the generator or transfer switch does not provide GFCI protection, the kitchen will not have GFCI protection when on generator power.