A couple of things we found useful in addition to the excellent suggestions above:

When applying local anaesthetic cream – rather than applying it directly on the skin, we found the easiest way was to put some on the sticky side of a clear dressing. Then stick the dressing on to the inside of the elbow. Much less mess!

Meeting a friendly play therapist one time we were in hospital was a great help. She showed our son how he could “take blood” from a toy bear. He loved doing this and seemed less scared by blood tests as a result.

These days – aged 12 – he’s fine with blood tests. The cold spray works well enough and his veins are easier to take blood from than they used to be. It’s all done in seconds.