Quick chemistry lesson:
Here's the structure of acetic acid: http://upload.wikimedia.org/wikipedia/commons/f/fd/Acetic-acid-2D-flat.png
Here's the structure of acetoacetic acid: http://upload.wikimedia.org/wikipedia/commons/d/d4/Acetoacetic_acid.png
First, note that the rightmost carbon of acetic acid, has a double bonded O and an OH attached to it. In chemistry terminology, this is usually written as COOH and a COOH group is an acid (carboxylic acid).
Look at the acetoacetic acid structure, you'll see a COOH on the left most carbon (it's not written out with a C here because they used shorthand where all unlabelled intersections of lines are assumed to be a carbon. So that COOH group makes it an acid. Then on the other end, there's a C double bonded to an O and a CH3 group. That's your ketone. Basically a C double bonded to an O is a ketone group (but it's not considered a ketone when there's the other OH group, you could say that the acid takes precident).
The reason you use ketostrips is to know if there are ketones in your urine. They specifically chose to measure acetoacetic acid, probably because it's an easy measurement, and use that as a proxy for all types of ketones present. But since acetic acid and acetoacetic acid have completely different structures, there will be no mixup in the measurement.
Also, I'm sure that the acetic acid you eat (as vinegar) gets broken down pretty fast in your digestive system, and doesn't last long as acetic acid in your body.
To answer your main question, I doubt it has any effect on ketosis. Your body will burn sugar when it's available. If it's not available, your body will turn fats into ketones and burn them. Having vinegar doesn't change the amount of sugar in your body, so if you're still low on sugar, you'll be burning ketones.
Think of it this way, your body will burn sugar or ketones with sugar taking precedent. This doesn't mean that sugar is the better fuel, ketones actually are the better fuel, but that sugar is so toxic you body will burn that fist just to get it out of your system.