Your question says we can find "this part of the book" in the link your provide. I don't find crickity, so I am answering about the word clickity, which is what I think you are referring to.
The opening line of the story includes the compound word clickity clack.
Splat's bike went clickity clack.
The word is usually spelt 'clickety-clack'. But since the word refers to a sound, there are variations in spelling. Dictionary dot com provides this definition:
[the] rhythmic, swiftly paced succession of alternating clicks and clacks, as the sound produced by the wheels of a train moving over tracks
In the story, clickity clack refers to the sound of the bike's wheels as the bike goes over "the bumpy track." The word can also refer to the sound of one or more typewriters.
The word can be spelled different ways, including 'clickety clack' and 'clickity click'. All these are examples of onomatopoeia, or a word that sounds like what it means. A computer mouse button and the shutter of an SLR camera make a click when you press them. Other examples of words that sound like what they mean from the opening pages of the story include Splat, whack, smack and, later, quack.
Video of the story being read to a kid: Splat the Cat and the Duck with No Quack.
Another way to get a clickity click noise from bike wheels is to attach playing cards to the bike frame so that the spokes of the wheels hit the card. But this makes a much faster clickity noise then does the sound of the wheels on a bumpy track. For example, see this youtube video. This is not what is happening in the story, but it is something that kids do.
Hope this is helpful!