Thomas Jefferson said a lot of things. He, like so many politicians, was not consistent.
He emended his famous speech about "watering the tree of liberty".

The difference in flying the American flag at lynchings and the Confederate flag has more to do with the intention of the lynchers. The Confederate flag being flown has a specific intention and that is to support a system of slavery and the inferiority of a race. The American flag has historically symbolized the opposite.

I think Jefferson would have understood Lincoln in the context of the Civil War and emended his statement.

I don't think that the UK in its entirety would consider the proposition that flying this battle flag would be a positive in light of the sociology of the US regarding its position on slavery.
In short, not one person can speak for an entire UK.