https://www.amazon.com/Godox-A1-Smartphone-Synchronizing-Radio-Enabled/dp/B074TCNJ1B is required to trigger it

Then you only really have one choice for flashes, and you won't get it under budget

https://www.amazon.com/Godox-A1-Smartphone-Synchronizing-Radio-Enabled/dp/B074TCNJ1B

That is a flash system made to sync with a phone camera. With it you can attach other Godox flashes for it, but you will need that to trigger them. So replace the speedlight with a https://www.amazon.com/Godox-Speedlite-Wireless-Transmission-Standard/dp/B0199F70RC for above and the wireless trigger with what is linked here.