I've just zinc plated some parts for a recumbent trike I'm making. The orangy yellow colour they've come out doesn't match the nice red colour of the frame, so I want to paint the outer tube the same colour as the frame. Do I need a special primer to stick to the zinc coating or can I use normal primer?

Smart51 after a period of time any paint on a zinc based surface will flake off unless you use an etching primer first.

Yes you do. I cant remember the name of the stuff but you paint it on and the zinc turns black. You can then paint as normal metal.

Mordant solution is what you need.
Turns it black and then it can be painted

We use some stuff at work called T wash, you just brush it on and it turns black then rince it down and once dry just prime over the top of it.

Plus one for T Wash

As above, an etch primer is what you want.
And I'm sure most people are aware that zinc plating is a 'line of sight' method, so if you have return bends or box sections on the part you have had plated, there is likely to be bare areas that have not been plated, so worth checking on any hidden faces that need extra treatment. The number of people that look at rust runs coming out of nice shiny zinc plated items and wondering how its possible is quite high.