However, if this is truly the start of a story, I'm not convinced you're starting in the right place. I say this because there is a lot going on that I missed.
For example his maladies. Crutch, headache, sprained ankle.
Then the main thing is his motivation. I'm sure you will get to why he's there, but my guess is it will end up being told or flashback. Not the end of the world, but starting earlier would solve all these issues.
However, they may just be my issues, so please only consider them if they make sense to you as well.
Axe
I wouldn't worry about your starting point. As a reader I can interpret Finkely's injuries as a result of his efforts of navigating the secret tunnels. As for the crutch it adds intrigue for the character.
It could use some line editing, but nothing major.
I do have some reserves about the voice in his head line. I would have to be able to read on to give this line more context.
Consider avoiding the negative phrasing of 'ached from not ducking low enough in one of the tunnels' with something like, 'ached from banging his head in one of the tunnels'.
'His sprained ankle pulsed, but only a little. It was on the mend'
That might read a bit more smoothly if tightened, something like:
His sprained ankle pulsed, but was on the mend.
Good luck with it.
PB
Frankly I liked it a lot. I think your choices give your writing a distinctive voice and I would not try to change that.
What you've got here already gets a lot of questions rolling in my mind, which is great: why is Finkley crawling through tunnels and chimneys? What is the 'job at hand'? How did he/she sprain the ankle - in the tunnels or doing something else? What is that voice in his head and why is it talking to him/her?
I think raising that many questions is a good idea; it hooks the reader and creates an immediate need for resolution.
Nice job; it makes me want to go back and make sure I'm doing the same thing in my own openings.
Good luck!
Respectfully,
History
The one thing that I sort of tripped up on was the first sentence. It seems to be in the wrong order or too long or..... something. Can't quite put my finger on it.
quote:
After five minutes of silence, and satisfied no one was in the library, Finkley lowered himself down the last few feet of the chimney.
I thought I'd change this to read something like:
"The library had been silent for five minutes. Satisfied, Finkley lowered himself down the last few feet of the chimney."
But the more I compare the two - the more your sentence fits with the rest of the tone of your first 13. I think it's the "and" that doesn't quite work though? I feel it comes too early. So, not quite sure how to fix it, or if it really needs fixing at all. Sorry, probably rambling a bit but just my two cents