The simplest commercial product for finetuning your own model is probably Adobe firefly, although there’s no API access support yet. But there are cheap and only slightly more involved options like Replicate or Civit.ai. Replicate has solid API support.

Check out:

https://replicate.com/blog/fine-tune-flux

Is it Flux 1 possible to download and deploy to my own server? (And make a simple API on top of it?) I don't need fine tuning.

The easiest flux api I’ve seen is with Fal.ai

It is expensive though- Flux dev images are like $0.035/image

If you have GPUs on your server that can handle it.