Verify you have the key on and the on off switch on
Verify the spark plug your using is good on another machine, even a lawnmower can be used. Have found brand new plugs bad from the factory...
On a FL350 first check for spark by removing the spark plug and pulling the recoil starter, using my fading memory the FL350 had problems if you have a weak or bad electric starter you will not get spark, the extra current draw from the starter affected the spark.
The next thing I do on a NO SPARK situation for Pilots, odysseys, motorcycles, snowmobiles, is to unscrew the spark plug boot from the spark plug wire then strip back about 3/16" to 1/4" of the spark plug wire and check for spark using the recoil starter, just hold the stripped end about 1/8" away from the head, if you have spark then cut the wire flush with the end of the spark plug wire, screw the spark plug boot back in and check for spark again with the spark plug attached. The problem usually is a bad connection between the wire and the part of the spark plug boot that screws in. (corrosion)
NOTE: Have a second person handy to pull the recoil starter so you DO NOT GET SHOCKED
Let us know how you made out.