Is it possible to fly an ultralight aircraft with a 13.4kW engine?
The earliest ultralights (hang gliders with add-on engines) used engines with as little as six horsepower (about 4 kW), possibly smaller.  That said, these aircraft were originally built as foot-launched gliders, and even so had safety issues and many incidents due to poor climb rates.

The main requirements for the engine in an ultralight are climb performance (which translates directly into takeoff acceleration) and reliability.  With the correct propeller and acceptable dry weight, an 18 hp (13.5 kW) engine might be acceptable, but every additional kilo of engine mass (compared to engines built for lightness) is one less kilo of structure, and the RPM figure given seems to point to a four-stroke engine, which will generally be heavy for its power output as compared to the two-stroke type.

Four-stroke engines have been used in larger aircraft for more than a century, but those are mostly engines designed and purpose-built for aircraft use.  An engine designed for garden or yard equipment, generator, or compressor service will usually be heavier.  You'll have more trouble finding an optimized propeller for 3600 rpm than for 5500, in that power range.  

In the end, if that's a cast iron four-stroke engine, it's unlikely you'll make your overall dry mass budget to stay within US Part 103 requirements without compromising structure, and you're likely to see performance issues with minimal power and maximum takeoff weight.