Flanking with Improved Whip Mastery

If I am weilding a Whip and have Improved Whip Mastery I threaten all squares within 10 feet. How does Flanking Work in this reguard?

What angles are acceptable to be threatening from to get flanking with an ally?

The acceptable locations don't change; they're the same as those shown and described here. You still have to be opposite your ally.

The relevant line from the flanking rules is:

When in doubt about whether two characters flank an opponent in the middle, trace an imaginary line between the two attackers' centers. If the line passes through opposite borders of the opponent's space (including corners of those borders), then the opponent is flanked.

You always threaten adjacently, so that works as normal.

You also threaten like a reach weapon would (assuming you're small or medium anyway)-Directly across from someone orthogonally or diagonally, as you'd have to be with just a 5' reach is good.

If you're positioned where a chess knight could attack, you can only flank who is also a knight's move away. Unless it's a large enemy or bigger in which case some funny angles start working out just fine.

All that said, this feat is yet another nasty complication in how the rules for whips clearly seem to assume that a normal reach weapon shifts your reach 5' out from whatever it normally is, as opposed to shifting your reach out past whatever it would normally be.

If you're positioned where a chess knight could attack, you can only flank who is also a knight's move away.

Actually, based on the line you quoted, if you're a knight's move away you can flank with someone orthogonally adjacent to your enemy, like so.