Without seeing or handling a scraper that has gone through a sharpening process and isn't working it is hard to diagnose what's gone wrong, but there are some common problems that you might be experiencing.
If the user is unable to create any burr at all1 I believe the most common issue (and the one I think most likely to be the cause here) is the prior preparation of the edge hasn't achieved 90° corners for the hook to be drawn from2.
So first thing you should do is make sure you are creating square edges on your scraper to begin with. Then the creation of a burr you can work with3 is almost guaranteed.
There are various tricks to ensure you'll get the square edges you're after, and most rely on some kind of block of wood to help hold the card upright. Instead of trying to describe this further in words I'll just link to two videos I think give good clear (and, importantly, brief) demonstrations of how to do it.
The first is an older video from StumpyNubs, and as usual for him he explains what he's doing and why very well. 5 steps for easy woodworking card/cabinet scraper sharpening
The second is one of a couple of vids on scraper sharpening on Fine Woodworking's YT channel. This one, How to Sharpen a Card Scraper, has Mike Pekovich demonstrating a nice simple method with one neat trick (courtesy of Brian Boggs) that is not often seen elsewhere.
Now both of these do show a vice being used, but you can easily work around this until you have a vice as long as you have some decent clamps.
If you clamp a piece of wood with a known square edge to your bench/work surface and then clamp the card scraper to that you have in effect created the same workholding that a vice provides. It may be in a slightly clunky and slower way, but it works :-)
1 None can be seen or felt, and the scraper won't produce ANY shavings.
2 If instead of a sharp 90 you have a sight radius along your edges when you do the burnishing it just moves metal into the space above the curved edge and it either doesn't create a hook/burr at all, or it's very small and isn't projecting far enough to engage with the wood.
3 Note that as I mention in the old Answer I linked to in the Comments, there isn't just one size and style of burr that will work. All different methods that successfully create some sort of burr are being used by someone, just for different levels of work and/or in slightly different ways. Some users want a very noticeable, very aggressive burr because it suits what they're doing, others need a very tiny burr that produces the most wispy shavings which show that only the tiniest amount of wood is being removed.