Yes , you can. You can kilz it with oil or latex , then paint with latex. Latex over oil paint/primer is fine. It's oil over latex in most cases that problems can arise.

It is latex over oil based FINISH paint that will give you adhesion problems and on the interior you can apply oil based paint over latex with no problems.

I am not sure why you are using Kilz at all unless you have some type of stain to hold back such as a water stain and the latex will not do this anyway. You can use a primer made by the company that made your finish paint and save some money and get a good job to boot if all you need to do is seal up the wall before you apply a coat of say eggshell/satin over a flat paint that is already on the wall.

Checked with acouple paint stores and sites ,, you can paint latex over oil or visa versa. The oil surface has to be sanded down for adhesion purposes but it works. Have done it many times in the past with no problems........... For interiors:
From Sherwin Williams Representatives email reply:::::::
You can safely apply latex over oil, or oil over latex, but only if the previous finish is (1) flat, or (2) has been sanded. If in doubt about what's there, you may want to cover first with a primer.

you can probably get 10 different opinions or responses. i found 4 different ones in about 10 minutes searching the web!!

Before you apply acrylic/latex over oil based finish paint you had better make sure it will work as there are some that will not stick even if you sand the surface of a semi-gloss or gloss oil based enamel.

I work for the Duron Paint company and we have 2 acrylic/latex semi-gloss paints ( signature select & genesis) that will adhear to oil enamels and and 5 that will not, so as you can see you can not make a blanket statement that all acrylics will adhear to oil enamel. So if someone goes into a home center and gets a clerk that was working in plumbing yesterday they may very well get the wrong paint and end up with a mess.

Have a great day.

Well experience overrides any techs advice I have been painting for many years and you can prime with oil or latex and use any top coat over it.I paint commercial and residential and have had many of the same contractors for ages and if there was ever a problem I know darned well that I would not be painting for them anymore.
People think it is always a problem such as if you use latex primer and oil topcaot that the latex will flex and such and the oil will not and thus oil will crack or break giving you a bad job I have never seen this and live in 1 of the most flexable climates their are ranging from 20 below to 100 degrees with high and low humidity.