To me it seems like returning chi-sq = 0 and p-value = 1 would make sense.
It would also be consistent with other scenarios of equal variance in all
groups. One example:

fligner.test(1:8, gl(2,4))
#        Fligner-Killeen test of homogeneity of variances
#
# data:  1:8 and gl(2, 4)
# Fligner-Killeen:med chi-squared = 0, df = 1, p-value = 1

But I am aware that other tests implemented in stats:: sometimes throw
errors in similar situations.

Maybe someone more familiar with the behaviour and philosophy behind
stats:: preferences can add more weight here?

Warm regards,
Karolis K.

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