Are you certain you are looking at an active listing that is still in stock?
I see a Buy It Now button in the eBay app and using a mobile browser when viewing active fixed price listings, or auctions that have that option and no outstanding bids.
Make sure you have the latest version of the eBay app.
Try another browser to rule out browser issues.
If you see the button in another browser, try clearing your cache in the original browser.
