I haven't heard much about the Fluval Flex, but it seems fine. If you want a lower-budget (and more customizable) setup, you could buy stuff separately and put it together yourself; it won't look as shiny as an aquarium with a premade stand and filter, but it'll work just as well.
Pet shops and your LFS might have sales like a dollar-per-gallon sale; it depends on the time of year, current circumstances, and where you live. If you take advantage of a sale like that, you can get a 30 gallon aquarium (similar size) for $30. Good sand substrate for that size tank might run you $15-$20, a filter might be around $40, and extra decorations/accessories/resources are pretty much up to you. Adding in the cost of a good API Freshwater Test Kit ($20-$30, depending on where you buy it), that's $110 before any additional accessories. Which is a lot, but considering the Fluval's $350 (and it's on sale right now), it could be a lot worse.
Building your own tank requires a lot of planning and prep, but if done well, you can save a lot of money. My whole 20-gallon setup for my axie cost me around $250-$300, and I know pre-built tank setups would cost more. Either way, your new axolotls will probably be alright- they don't care how much their tank cost, they care about if the tank is cycled and if there's light/excess waterflow/etc.
Welcome to the forum, and best of luck caring for your new adoptees!