Unfortunately, it's not so much what is in the coil fins to flush out, but the debris that can mat up in the gap between the CAC and the radiator.
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I remove as much as I can up front for access, without losing fluids, then go after it with a long 2' blower gun extension thru the sides (where available)and back from the engine forward to the grill. Has a rubber tip that helps prevent damage to the fins.
Then I go after it with water Volume, not pressure to flush/rinse, from the front, the sides, and from the engine bay forward, using an open garden hose (no sprayer).
Next is a soak down of cleaner, I use SGreen but there are coil cleaning products on the market that are 'hotter' as far as clean action and bug/grease dissolving.
After a good soak period (never let whatever cleaner/solvent you use, to dry), I go back after with the volume hose again for the final rinse.
Finish up with the leaf blower to move/extract any and all water collecting still in the fins AND the lower fan shroud too (makes a mess on startup otherwise).
However, none of this ^^ helps if all you have is a truck wash bay out on the road with no compressed air to work with and nothing but high pressure/low volume water sources available. Downerrr