I used the unrecommended method of installing on a non-SSH enabled shared hosting service. I have been able to run Flarum on HostMantis.
Excluding my domain registration, HostMantis with coupons costs me approximately $15 triennially for their Linux unlimited shared hosting plan. That is right: unlimited storage and unlimited bandwidth for the cost of peanuts.
I have had no issues with speed or reliability with this hosting service for the last three months. For what I can see, they still have an 80% off coupon (SPRING18) and it works for their unlimited shared hosting service below. At the triennial rate with this lifetime coupon applied, you pay $15.19 instead of $75.95 every three years, which comes to only $5.06-$5.07 per year.
HostMantis is the best bargain I have found for unlimited or high storage (>10GB) hosting after years of voraciously reading Web Hosting Talk and speaking with many people in the industry. There is also StableHost, but they cost a bit more. But they offer SSH for their shared hosting plans:
https://my.hostmantis.com/cart.php?gid=44
Keep in mind that most any free options out there will have major drawbacks, meaning gravely throttled down in IO and CPU performance. It may take upwards of 15 minutes just to install an extension, for example, given these free service’s slow bandwidth.