Slitherine

If there is a combat close to a unit defending a building can it give flank support?

I suppose it all depends on whether a unit in a building generates a "support area". I think the answer is no.

The building FAQ states in the section Firing to and from Buildings under Dice Modifiers that there are no support dice when shooting at of from buildings (4th bullet point).
It further states in the section on combat against buildings that neither side can receive flank support.
They can receive rear support, but this is not determined by the support area.

Based on these (even though it is not explicitly stated), I think you can say that the "support area" cannot cross the boundary of a built-up area.
This makes sense, considering that so much changes when a unit is defending a building. And a unit in a building has a much larger footprint than one which is not, and it would be a little unfair for such a unit to suddenly spread a support area over a much larger space.

makes sense to me. Just is not stated explicitly in the rules.

I agree it makes sense. Buildings are hard enough to crack as it is.