I could be wrong, but I'm pretty sure I'm right about the following:
1) Flannel doesn't make it much if at all less formal. It makes it wintry.
2) Flannel plus those trad details plus brass buttons doesn't make it discordant. It's a very classic configuration, sold for decades by stores like Brooks Bros.
3) Those trad details do and do not make it informal (as far as blue blazers go). This blazer could be worn well with anything from white shirt, repp tie, and mid gray worsted wool pants to well-worn ocbd, no tie, and rumpled cotton chinos, cords or faded denim -- with or without a fine merino sweater for the formal side or a shaggy shetland for the informal. So its range reaches as high as what might be considered the most formal of blazers, but it also reaches down pretty low. A good argument for its purchase.
This sums it up. What you have is a classical blue blazer. If it has patch/flap pockets it is modeled on the Brooks Brothers garment sold in the University Shop and the 346 Shop during the Ivy heyday..