If you have no experience in sound design, I'd suggest buying a pre-made sample library. That way, you will have access to a library of sound effects for any future projects. You may be able to buy individual samples if you don't want to buy a whole library.
You could search online for free samples, and I'm sure you would find something you like, but you may not be able to use them in comercial projects. Some sites like SoundBible offer truly royalty free samples, but you may find they are limited or lacking quality.
As for your question about FL studio, you create FX sounds the same way you create any other sound in FL Studio; with built-in or third party VST instrument plugins.
I couldn't say specifically which VST to use for button effects, I use the same VSTs for everything I do really(technically, VST plugins are effects and VSTi plugins are instruments). You can create a button sound effect easily with most software synths though. Even free ones. They are usually really simple sounds. If you're stuck, find a similar sound, maybe from a similar app, then ask someone how to make it. Or I'm sure there are tutorials out there that could help you. Some button effects are simple, soft, static tones(no movement) with a short decay, but they can be more complex.
I'd just get a free VST synth and try a few presets out and mess around with it, see if you can get a sound you like. Adjust attack and decay to get a short, soft sound. This free analogue synth is just one of MANY I found with a simple Google search.