Is $4,000 to flash a chimney a fair price?

I have a rental property that is leaking, and I'm in a bind needing to get the issue resolved fairly quickly. I was shocked by the price tag for the initial quote. The previous owner apparently didn't flash the chimney when the roof was put on. I recently had a whole roof done for $10,000, so this new quote really surprised me. It's a steep roof, but from what I understand, the chimney doesn't need to be repointed. My theory is that the chimney was tarred, which is why it's not currently leaking. I just bought this house this year and don't know the original installation details. No one has physically been on the roof yet. The chimney itself shows no signs of leaking, and I plan to remove it within a couple of years. The person I ultimately hired has worked on the roof before for the previous landlord. I believe the first company either didn't want the job or is accustomed to customers not questioning such high prices.