I have read the following sentence:
My uncles are flower vendors.
Would it be incorrect/unusual to say "flower sellers" instead? If not, is there any difference between both (e.g. having a shop or working on the street)?
Essentially both seller and vendor mean the same thing. Vendor is of French/Latin etymology while seller is from Old English.
Though with such duplicates we do love to look for shades of difference in tone or feel that even native speakers might argue over. You wouldn't really ever be wrong to just use seller and stick with it.
Given that caveat, if forced to make a distinction, I would put it something like this:
Vending has some sense of being more organised, formal or systematic. You are more likely to call someone a vendor if selling in larger volumes, or as a manufacturer, wholesale etc. Other very common use is when talking about sale of property.
Very casual or informal occasions or smaller scale activities are more likely called sellers.
You are as also more likely to talk about "sellers" from a consumer perspective and "vendors" from a trade perspective.
So you wouldn't really ever be WRONG to call anyone sellers or vendors, but yes, a flower vendor would be a little more likely to have a shop or wholesale business than a flower seller. But there is no hard and fast difference you could rely on.
I think Duke's answer covers much of the important distinctions.
It is hard to find a difference between them based on definitions.
From Merriam-Webster -
a person who sells things especially on the street
a business that sells a particular type of product
From Cambridge -
someone who is selling something: For the past few months she's been working as a street vendor, selling fruit and vegetables.
This Amazon article might be of interest: Vendor Vs. Seller: Which one should I choose for my business?
From the article, it seems like one distinction between the two is the scale of the sale. Sellers are small third-parties and can sell independently. Vendors sell in large quantities. This however is not a reliable distinction, as Peter Jennings, MW, and Cambridge dictionary says, "street-vendor" is often used to refer to a small scale independent seller.
Amazon Seller Central allows “third parties” (third-party seller) to use Amazon as a marketplace, to list products there and to sell them independently. They have full control over their product listing and price. . . .The goods, however, belong to the dealer at all times and are only available in Amazon’s warehouses until they are sold and processed.
A retailer that sells via Amazon Vendor Central is called a first-party retailer. Companies are like suppliers and products are sold on Amazon in large quantities. After the sale, Amazon becomes the owner of the goods and takes over the responsibility for marketing, sales and price. This means that the retailer becomes dependent on Amazon. Vendor Central is invitation-only and is primarily intended for major manufacturers and well-known brands.
What is interesting is how the use of "vendor" and "seller" changes with what they sell.