If a character takes the monk as a secondary class as shown on p. 89 of Pathfinder Unchained, they get the Ki Pool class feature with a number of ki points equal to 1/2 their character level. But can they do anything with those ki points? They don't gain any of the monk's ki powers, but can they expend a ki point to make an additional unarmed attack even though they don't have flurry of blows?
Ki Pool (Su): At 4th level, a monk gains a pool of ki points, supernatural energy he can use to accomplish amazing feats. The number of points in a monk's ki pool is equal to 1/2 his monk level + his Wisdom modifier. As long as he has at least 1 point in his ki pool, he can make a ki strike. At 4th level, ki strike allows his unarmed attacks to be treated as magic weapons for the purpose of overcoming damage reduction. At 7th level, his unarmed attacks are also treated as cold iron and silver for the purpose of overcoming damage reduction. At 10th level, his unarmed attacks are also treated as lawful weapons for the purpose of overcoming damage reduction. At 16th level, his unarmed attacks are treated as adamantine weapons for the purpose of overcoming damage reduction and bypassing hardness.
By spending 1 point from his ki pool, a monk can make one additional attack at his highest attack bonus when making a flurry of blows attack. In addition, he can spend 1 point to increase his speed by 20 feet for 1 round. Finally, a monk can spend 1 point from his ki pool to give himself a +4 dodge bonus to AC for 1 round. Each of these powers is activated as a swift action. A monk gains additional powers that consume points from his ki pool as he gains levels.
Above is what is listed under the Ki Pool of the monk class. Since he does not have the fluffy of blows class feature, he cannot use a Ki Point to gain the extra attack, but he can use it for the increased move, and the +4 dodge bonus. His unarmed attacks are also considered magic, cold iron, silver and Lawful at the appropriate level and if he is Lawful for the Lawful.
You could combine this with elemental ascetic kineticist to get the flurry of blows. The two have surprisingly good overlap actually.
I assume you are using Variant Multiclass (VMC) alternate rules
Yes, that's the page he was quoting.
Variant Multiclass is mostly just for fun, as the options aren't that strong. But it is interesting how well it lines up with elemental ascetic. Neither are that great on their own, but together they are more appealing.