my mom's black reissue has a double flap and the inner flap is burgundy lining. the bag is calfskin.
my grey reissue (also calfskin and double flap) has grey lining.
my new classic mini (single flap) is totally black inside.
I believe when I tried on a black caviar jumbo flap at NM's, my SA said the double flaps came in both colors, some with black and some with burgundy. I did not inquire too much since I did not plan to buy a jumbo at that time but I can ask next week when I pick up my mini.
Actually, I just purchased my first Timeless Classic Flap in black caviar last month and the interior is burgundy (from the actual store, not online). The ladies working at the Chanel Boutique in Venice explained that all of the Timeless Classics have burgundy interior, when I'd asked if it came in another color (I didn't care for the burgundy). That's how you know it's a classic flap, apparently.
I did notice that the other bags had black or grey satin interiors, but that was special bags like the Patchwork Flap that was just released. I have an older bag from the Paris New York Collection from 2005 or 2006 and that is lined with black satin (exterior is tweed).
If you want to know for sure, give any boutique a call and they will happily answer
Some hologram stickers are hard to see in these bags. I didn't see it at first when I was in the store and the sales associate had to almost turn the bag inside out for me to see it.
On my Paris New York Tweed bag, the interior is satin and there is an actual tag with the hologram attached. It's on the left side, I believe (without looking inside of my purse). It's also on the left side of my Classic Flap, but it's stuck towards the very bottom in the main compartment (left side) on the actual leather.
So, I believe that there is a fabric tag with the sticker on ones lined in satin and leather bags just have it stuck inside on the left.