I would say a flame angel is too large for a 25gallon tank. It hits 4" in length...I'd keep it in nothing under 30gallons...though 40+ would be 'ideal'.
Any amount of ammonia or nitrite is bad for fish...that's why cycling with fish is never recommended.
If you plan to swap fish, I'd quarantine the clown for 2-4 weeks. If you introduce a sick fish (for example, one with marine ich) to your display tank, you'll have to remove the fish to medicate it, and then run the display tank fallow (without fish) for 6 weeks to ensure no parasites are still alive.
However to directly answer your question, change the water first, then add the fish. Acclimation is stressful, and following it with a water change could push the fish over the edge.
Former advisor and planted tank geek...life's moved on though.