From the source

Fine-tune FLUX.1 with your own images

Capability change

Image published with the post by Replicate — Image from replicate.com

Replicate announces that users can fine-tune FLUX.1 models using Ostris's AI Toolkit, which employs LoRA for fast and low-cost training (under 2 minutes, under $2).

The post provides instructions for preparing training data and running fine-tunes via the web or API.

From the source
You can now fine-tune models with the fast FLUX trainer on Replicate. It’s fast (under 2 minutes), cheap (under $2), and gives you a warm, runnable model plus LoRA weights to download.
replicate.com