Are there any remaining flying boat or seaplane airliners in operation?
As far as I know, there is no actual flying boat in use at an airline. The flying boats that are still in commercial operation are typically used for fighting forest fires or maritime patrol. This may change in the near future since there are currently at least two flying boats in development that might be used by airlines:

Dornier Seastar CD2: This is a newer model of the previous Seastar, which had its first flight earlier this year:

Dornier Seawings flew its new-generation Seastar amphibian for the first time on 28 March from its base in Oberpfaffenhofen, Germany.
[...]
Dornier says the aircraft will be offered in various configurations including cargo, passenger, special missions and VIP transport.

(flightglobal.com, emphasis mine)

AVIC AG600: This is new aircraft developed in China and one of the biggest flying boats ever. It had its first flight in 2017 and according to Wikipedia is expected to be delivered by 2022, possibly also in a passenger variant:

Further variants may be developed for maritime surveillance, resource detection, passenger and cargo transport.



If you are not just interested in pure flying boats, but also floatplanes, then there are many airlines world wide that operate these on regularly scheduled flights. One of the biggest is Trans Maldivian Airways operating various variants of the DHC-6 Twin Otter. They operate 55 seaplanes, which according to Wikipedia makes them the biggest seaplane airline:

TMA currently operates the world's largest seaplane fleet.

They offer flights to over 80 destinations:

Trans Maldivian Airways currently offers transfer services to more than 80 Maldives resorts, flying over 1 million passengers per year to their holiday hideaways.

(transmaldivian.com)
This is their main terminal at Velena International Airport:

(image source: Wikimedia)