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He was holding the focus sash and was using Head smash on Togekiss who used air slash on him with Serene grace and bright powder. Based on an ingame battle against Cheren.

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Air slash normaly causes flinching 30% of the time. With Serene Grace, that gets multiplied by 2 for a total of flinching 60% of the time, or moving 40% of the time. The evasion is raised 10% due to the bright powder, givig you a 90% chance of hitting. Head smash has a 80% accuracy to begin with; if you don't flinch. To combine these threefactors, we do some multiplying:
40/100 not flinching x 80/100 accuracy x 90/100 evasion = 288000/1000000, or a 28.8% chance of hitting. If I did the math right.

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This is *almost* correct. Head Smash is 80% accurate and BrightPowder makes you 90% accurate on normal moves. Therefore it's 0.8*0.9 = 0.72 = 72%. Coupled with Air Slash that's 0.4*0.72 = 0.288 = 28.8%, closer to 29%.

EDIT: clever Fritjof, you beat me to it!
Yeah, I realized it too...  Looks like I was fixing it when you commented...
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You would have a 30% chance of hitting. Air slash with serene grace makes you flinch 60% of the time. Bright Powder makes you hit 10% of the time less. So 40%-10%=30%!

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You forgot to account for the fact that Head Smash has an 80% accuracy, not 100, plus the acuracy and flinching don't stack exactly like that.
You don't add/subtract probabilities, you multiply them.