Hi Adrien,
It is possible to upload your custom integration with the Fleet package upload API: Fleet APIs | Fleet and Elastic Agent Guide [master] | Elastic
Here is an example:
curl -XPOST -H 'content-type: application/zip' -H 'kbn-xsrf: true' https://KIBANA_HOST:PORT/api/fleet/epm/packages --data-binary @custom_integration-1.0.0.zip