Reddit mentions of Humminbird 410210-1 HELIX 5 CHIRP GPS G2 Fish finder

Gonna go a different route from the other guys. This isn't the exact one I have, but I'd look at Humminbird's Kayak line of fish finders instead of their ICE line or larger boat stuff.

The HELIX 5 looks like a good option at a good price: https://www.amazon.com/Humminbird-410210-1-Helix-Chirp-Finder/dp/B01M2VLBQF - or the NON-GPS Version + the Navionics App (15$ish, IIRC?) on your phone: https://www.amazon.com/Humminbird-410210-1-Helix-Chirp-Finder/dp/B01MCWIC5H?th=1

Just about any sonar you get nowadays will have a digital 'flasher' dial as one of the screen options and I've found it works just as well as a FL8/VX-1. On top of that, you can actually use it in open water because it has a normal 'sonar' just like you'd see on an open water boat.

Truth be told, I've ended up using the open water sonar more often than the flasher dial anyway. It gives you a little bit of 'history' so you can see what types of movements you were doing when you finally triggered that fish to raise up off the bottom and inspect your bait. Typically the open water sonar has a vertical column along the right side of the screen that acts exactly like a flasher would, so I just use that so I get both the flasher aspect as well as the history aspect.

You'll need to get some sort of a 'conversion kit' to make the flasher work properly for ice fishing, but that kit usually includes a carrying bag, mounting platform, etc, just like you'd get with an FL8 or similar, and shouldn't cost more than ~100$.