I'm afraid I'm not sure what "Chukker" boots are! Some time ago, here in the United Kingdom, Chukka boots were quite popular and were worn with trousers, and they might still be, but I've not seen them for years.

My general rule (yes, I know there are no rules!) is Shoes: hose worn up and Boots: hose worn down. For me it is the visual appearance that matters here and, to my mind (and eye) hose worn down with shoes looks dreadful, and hose worn up with boots only slightly better.

As always, it is entirely up to the individual - and I stick to the above, every time!

Take care,
Ham.