Disclaimer: the climb to the top of Kahlenberg is not an easy one, at least not my preferred route.
The climb starts as soon as you take a left turn off of Greinergasse onto Hackhofergasse in Vienna's 19th district. There are two major sections to the climb, separated roughly in half with a short descent. The lower section is steep, especially in the beginning where it ramps up to gradients between 15-20%. Hackhofergasse bends left and turns into Eichelhofstrasse. Passing under a tall stone arch the road kicks up dramatically, here is the most extreme gradients of the climb and it is extremely easy to go too hard here and run out of gas quickly. As the gradient mellows (to the around 8%) The route to the top forks to the left onto Eichelhofweg. It feels much more human on this section and is a good place to catch your breath while riding tempo. The view opens up here to expansive vineyards with Vienna on the left and Klosterneurberg in the distance on the right. Around the halfway point the climb tapers off before a short descent into the heuriger zone (a heuriger, by the way, is a fantastic place for a good meal and fresh wine) where the road merges and turns into Kahlenbergerstrasse. From there, the road ramps up again for the second half of the climb. The trees fill in again as the road narrows. There are with steep sections again around the 3/4 mark and at the very end.
Overall Kahlenberg is a fantastic climb. It has sections that are so steep you have to crawl up them. Depending on your pace it will put a noticeable tingle in your arms and taste of blood in your mouth, especially on the lower sections. However, the view from the top is worth it, as well as the satisfaction of knowing you just climbed one of the steepest and most challenging paved roads in Vienna (though there are harder, particularly Eisernenhandgasse to Kahlenbergerstrasse, though I have yet to meet someone who has finished that climb on a road bike).
Here is the Strava section for reference: