I'm not buying anything today (28th). I'll also not buy anything on whatever future buy-nothing days are planned.
A lot of the people who are saying this isn't going to work are assuming logical consumer behavior. If you were going to buy something, it was because you need it, and you're still going to need it tomorrow, so you're going to just shift your purchase from Friday to Saturday or whenever you get around it.
The first lesson of consumer behavior is that consumers are not logical. They are predictable and understandable, but not logical. Basically all of the consumer-focused classes in my marketing major included the professor ranting at some point about the economic rationality assumption.
There are two ways that buy-nothing days work: by removing some portion of total economic activity, and from participants identifying as part of an in-group that will lead to other behavioral changes.
There are plenty of purchases which, if not made today, won't be made up in the future: meals, impulse purchases, point-in-time events, etc., and then there's also the add-on economic activity. If you don't go out to dinner and a concert tonight, you're not going twice tomorrow, and you're also not using that gas and parking or paying for that transit ticket.
Have you ever wondered why stores will set up free memberships that give you perks? How is it possibly worth it to write my name down on a membership card and give me 5% off, when you could just get my name off my credit card? It's because a sense of belonging changes human behavior. People who participate today (in either signing up for a membership or joining a buy-nothing day) are more likely to take future action consistent with that belonging (continuing to shop at that store, taking other protest actions).
There are people at Amazon, Target, Starbucks, etc., watching today and this week closely. They will measure today against the past sales for this date, adjusted for other trends and marketing investments. They will know how many sales were shifted to tomorrow (represented by an increase in tomorrow's sales compared to the past), and therefore know how much of that was truly lost economic activity. They will also measure sales totals and visits for specific demographics, and project that out over the total sales for those demographics. If there's a drop in sales today to suburban women age 35-49 that's balanced out by increased sales to rural men age 18-25, they're also going to take what they know of the spending habits of both demographics to consider whether that's a shift in customer focus that will be beneficial in the long run. (If it's that specifically, probably not, middle-aged women are a sought-after demographic because they tend to control household spending.)