I mean, it's not going to be very strong, certainly not One Piece levels of strong, but it's possible. There's a very notable problem at the beginning of this thought experiment, namely soft things have a very hard time cutting through harder things. For instance, a knife through butter works very well, because stainless steel is a lot harder than churned milk. On the flip side, take a butter knife and try cutting through a chunk of titanium - suddenly a lot harder because as you increase the force, the knife breaks instead of the titanium.
The way to get around this problem is by condensing the material and increasing the force which is the principle behind a waterjet, and thus now water beats titanium. So, if we increased the the pressure of the air and the force, we'd get a more effective blade and now it's essentially just an air gun, minus the pellet.
Now, if you take a bunch of these and line them up, you get a facsimile air blade, albeit a terrible one that can only cut through soft objects, and maybe not even thought. That's because air is a terrible projectile - it freely interacts with the air around it (seeing as it is air) and has a lot of air resistance. In the end, it'd be no more efficient than trying to shoot a water gun under water.
Now, to get around this, we start cheating by stopping with this normal everyday variety of 'air' and swap to a better gas - sulfur hexafluoride, a very heavy gas and chill it to -63 Celsius, right above when it would start turning into a liquid. Condense, pressurize, and fire. Admittedly, this would need a massive contraption to use and would be inferior to the aforementioned waterjet, but you'd get the 'flying slash from a compressed air blade', and that's what counts at the end of the day.