Flame test for copper salts
There is a famous saying that paper never refused an ink, which means anyone can write anything on the paper and the paper won't say anything back to the writer. Internet has made this situation worse. One should develop a healthy level of skepticism when reading website and forums. 


  Why is copper the only transition element to give a coloured flame? Most other flame tests are given by alkali metals and alkaline earth metals, which is understandable and is a common trend across the group. Copper stands out as an exception.


This is not true. Boron compounds, when burned in alcohol, burn with a similar green color. Now here is the fundamental point to understand. When we see colors in the flames, usually it is due to very simple molecules of those metallic compounds in the flame. It is a molecular emission. If you can buy a pocket spectroscope, you will just a broad bands of color. So a flame spectrum, specially a low temperature flame, is not equal to an atomic emission spectrum. If I introduce copper into a very hot flame (>2000 Kelvin), you will not see anything, because copper atoms emit light mainly in the UV range.  

Therefore all the common flame tests with calcium, barium, strontium show the flame emission spectrum of simple diatomic molecules of Ca/Ba/Sr in the flame. Copper is no exception. You may also wonder why a hydrocarbon flame is blue, there is no transition element there?

Vanadium is yellowish green

Cerium makes the flame yellow

Lead is blue white

Yttrium is beautiful crimson, which often appears on textbook covers on inductively coupled plasma spectroscopy (very high temperature atomic emission). Wikipedia has a big list.

Atomic spectroscopists use Grotrian diagrams to assign the transition lines the emission spectrum. Nobody uses VBT to explain the spectrum. Predicting the correct emission spectrum even of a diatomic molecule in the flame, will perhaps require the knowledge level of a PhD in physics.