How do you thicken sangria?
You don't. Sangria isn't thick. It's the consistency of alcohol, which is less thick than even water, which isn't thick. Sangria is red table wine, liquor(s), and sometimes an added fruit juice all poured over bite-size chunks of fresh fruit that sit in the bottom of the glass or pitcher to flavor and to garnish the drink. The specifics of those ingredients can vary--like the kind of red table wine, the kind of liquor(s), the kind of fruit juice, and the kind of fruit--but those are the staple ingredients that make it sangria. Incidentally, I've had sangria in Spain, Italy, and Brazil. By far, my favorite was from Brazil. There must be a recipe because no matter where I went in Rio, it tasted the same. I know the wine wasn't Rioja, like they use in Spain. I know that it contained Cachaça, a Brazilian liquor made of fermented sugar cane. I know the chopped fruit at the bottom was heavy on orange and apple. Beyond that, I don't know. But if you look for a Brazilian sangria recipe, look for those aspects to be sure you've got the OG and not somebody's bastardized version of it.
Sangria is not supposed to be thick. It should be or close to the viscosity of wine. It may become a little thicker due to some fruit pulp but it would not thicken it enough to notice