The restriction is only applied to one class's features
The Scarred Monk says:
A scarred monk cannot spend ki points to make an additional attack at her highest attack bonus when making a flurry of blows, to increase her base speed, or to give herself a +4 dodge bonus to AC, nor can she use any of the other powers normally granted to monks that utilize their ki pools.
While monks normally are able to use their ki for these effects:
- Enhance his melee damage with certain effects (magic, cold iron, silver, etc), also known as ki strikes;
- Make one additional attack at his highest attack bonus when making a flurry of blows attack, or; (Not allowed)
- Increase his speed by 20 feet for 1 round, or;(Not allowed)
- Give himself a +4 dodge bonus to AC for 1 round.(Not allowed)
This means that the monk can only use their ki powers to make ki strikes and to use the archetype's Mortifications.
But when you become a Ninja (obligatory reference), you also gain a ki pool that can be used to fuel certain ninja abilities:
- A ninja can make one additional attack at her highest attack bonus;
- She can spend 1 point to increase her speed by 20 feet for 1 round;
- Give herself a +4 insight bonus on Stealth checks for 1 round.
While some are similar to a monk's usage of ki points, they are ultimately not the same abilities, those are ninja abilities and unrelated to a monk's usage of ki points. So the restriction that applies on the monk archetype will not affect ninja abilities and her usage of ki points.
Additionally, we also know that a ninja's ki pool will stack with ki points granted by any other class, into a single combined pool:
If the ninja possesses levels in another class that grants points to a ki pool, ninja levels stack with the levels of that class to determine the total number of ki points in the combined pool, but only one ability score modifier is added to the total.
But not only that, the ninja also says this:
The ninja can now use ki points from this pool to power the abilities of every class she possesses that grants a ki pool.
Which means that the ki point points granted by your ninja class levels can be used by any other class that also has a ki pool, including monks (archetyped or not), and these points have absolutely no restriction. Those points are fueling the Scarred Monk's ki pool, and thus can be used for mortifcation or ki strikes, while also fueling the ninja's ki pool and can be used to fuel ninja abilities.