I have been researching distillation lately. I am somewhat surprised at how it has increased my general Brewing knowledge. For example I heard on one podcast that tannins (extracted from the oak barrel) contributes viscosity, which in turn increases the length of the finish (flavor).
So I’m now wondering how I can get tannins into my beer without the actual tannin flavor (I’m thinking bitter or mouth drying). Thoughts?
That mouth-drying sensation is astringency/mouthfeel and not flavor. In something like whisky or a big red wine, it is something that is expected and enjoyable (when present in the proper balance). That is exactly the opposite of what I’m typically looking for in beer. If you’re looking to boost viscosity/mouthfeel in beer I think you’re better off shooting for more dextrins than tannins.
Buy a bottle of liquid tannins and play with it in the glass. A little goes a long way
That makes sense. Dextrins are unfermentable sugars/starches, correct? So mashing high and maybe some caramel malts…yeast choice also comes to mind. Anything I’m missing?
I guess the big takeaway is that viscosity increases length of finish.
I’d just be cautious extrapolating that to beer from spirits. The types of beer where I’m looking for a lingering finish (English Barleywine, for example), are already plenty viscous enough. It may help in a beer that feels thin or the flavor drops off too quick, but I don’t know if it’s always a “more is better” situation.
Much like how we make diacetyl out to be evil, tannins aren’t necessarily bad in beer. There are probably just as many references to tannins being noticeable in British styles as there are about diacetyl being present.
I won’t judge you for enjoying either diacetyl or tannin in your beer, but I don’t necessarily share your tastes on either. 
That said, the earlier suggestion to dose in the glass is probably worth an experiment. I’d be interested in hearing the results if anyone tries it.
Honestly, I think the tannic affects of using large amounts of low-alpha hops is part of why British beers benefit from oxidation so well. Kinda like letting a really tannic red wine breathe a bit before serving.