I'm running OpenSUSE leap 15.5, When I was on the linux mint, I was using warpinator but using it on openSUSE is troublesome and I wish there was a linux version of blip but unfortunately there is not.
I usually have a lot of troubles with KDE Connect no matter what device I'm using. Could be running windows 10 or Linux. I also sometimes have the files not transferring problem and even have had plenty of problems getting it to connect to devices that are in the same room on the same network. It's infuriating and makes me wonder why I even use it.
How big? When I'm lazy and the file isn't large I just upload to a draft email and look at it on the other device. I use Windows but this isn't really an OS specific method.
If by wirelessly you mean via Wi-Fi network then one convenient option is qrcp. It generates a QR-code right in your terminal, which you can scan with a phone and send/receive files through a web interface on the URL it provides.
If you want to transfer files regularly, there is another option. Almost every distro has Python installed, and the Python has a "built-in" FTP server.
You need to just cd into desired directory and run the command python -m pyftpdlib -w. It will open a FTP server with root in this directory.
You then can access it through a file manager, like Material Files for example, and send files and folders back and forth. In Material Files you can save the server address for future use.
I've heard plenty of other people have had a better time with it than I have, but I like to use KDE Connect for some reason that I'll never understand. That, and Wormhole, through flatpak since I suck at installing through source.
I drop files I want to share in ~/public_html/files/ as I have a webserver running on my desktop with the firewall open to the local network. Might be tough for a noob to setup though. But on my phone the file shows up in /~christopher/files/ and I have trouble remembering how to type the tilde.
I guess i depends on how much data you need to move and how long you want the sync open for. I've had a dropbox account for... I forget how long, and have never paid them a dime.