Here is some history of the coat of arms of Northern Rhodesia given in 'A brief guide to Northern Rhodesia', which you can read on the internet archive (p.132).
We are told that the fish eagle flying with its prey over a representation of the Victoria Falls harks back to David Livingstone's exploration as a forerunner of the European settlement here. The white lines represented the water, and the black lines the rocks of the precipice.
Discussion of designs for a coat of arms began in 1925, when one suggestion was for a representation of the constellation Orion, 'a mighty hunter who drove all the beasts of the field before him', on the basis that this was 'a prowess which distinguished most early Rhodesians.' In 1926 further design ideas rejected were a river scene (not suited to heraldry) and the sable antelope (already used by Southern Rhodesia). Any animal less than an elephant (as used by the paramount chief of Barotseland) or the buffalo (as used by Lewanika) it was said would be 'noticeable in African eyes', but a lion was not possible as that was used in Great Britain's royal arms.
In 1927, discussions between Sir Richard Goode and a heraldry expert yielded the design above. It was drawn by G. Kruger Gray to Sir Goode's design and accepted in the same year, being also approved by King George V in 1930 and granted as armorial bearings in 1939.
On this heraldry site it is pointed out that some people objected to the 'dead fish' the eagle held. There are connotations of colonial plundering in the eagle holding its prey in this way, though it seems unlikely that this was ever considered when it was drawn. More likely the fish was added to make clear that the eagle was a fish eagle and to signify the fecundity of the land.
The same design can still be seen in part in Livingstone's coat of arms, where Dr David Livingstone is one of two figures holding on to the shield. Here there is also an African man with a paddle, probably a royal paddler from the Lozi tribe, as would paddle the royal barge during Kuomboka.
fairly recent stamp issue depicting the coats of arms of the 'four most important Zambian cities' - Kitwe, Ndola, Lusaka and Livingstone. It has also been pointed out that, of course, fish eagles are black and white, and not gold, as the eagle has later been interpreted. Now there is also no longer a fish in its talons. (However, the fish eagle is the national bird of Zambia and Zimbabwe, and its call is used as the calling signal on at least one Zambian radio station.)
The legend says Procedens Floreo, that is, proceeding to flourish or prosper.
I am stumped by the circular cog at the bottom - could it be a paddle wheel? (I was very tempted to go into a long discussion of Livingstone's famous phrase 'I am prepared to go anywhere, so long as it is forward.')
It seems though that there is another interpretation, in which Livingstone's head emerges weirdly from the river and a man and a woman hold the shield, as on the national coat of arms.
The same design of water falling is also seen in the more familiar Zambian coat of arms. I well remember learning the meanings of the various parts of this when I was in primary school. Here again we have the golden eagle, or at least an eagle coloured gold, given that golden eagles don't occur in Zambia. This is also said to represent the abilities of the country to rise above its problems, as for the eagle on the Zambian flag.
As I was leaving Lusaka airport recently I suddenly realised I had all the coats of arms right in front of me on the wall! However, at the last minute I contrived to take lousy photos of them. I include a couple more below that weren't so bad:
Kitwe's says 'Let us build a city', Chingola's says 'Servire Creare Et', and Kabwe's 'The eagle carries us on high'.
It is interesting that on the Livingstone coat of arms there actually appears to be something more like a river flowing over the falls! It is tempting to think that the bars across the falls are the railway bridge, but they do not resemble the bridge, which you can see below:
If you look closely, you will see some bungee jumping going on! This is taken from the 'boiling pot', the part of the gorge below the falls where the water is funneled through from the main cataracts. Here you can also start white water rafting trips, depending on the time of year.
It will probably take someone familiar with heraldry to demystify the Livingstone coat of arms further.