An artifact, planet Flux is said to hide one of my planets from the scan lists of all other players.
Does it mean that it will Hide it from everyone else in the exception of myself permanently?
A way to permanently secure one of my planet?

Yes, with the exception of you

However, nothing is permanent... Someone can always find it again through another scan. You can use Flux Probes to check this.

is there a way to permanently block its appearance from anyone's scan?

You can increase the planet's cloak to reduce the chance that it will not be found, but there is no permanent way to prevent a planet from being scanned for or invaded. Of course, you can always use more Planet Flux

Awesome, sad but realistic . is there a way to get more planet Aegis? its effect seems very promising.

Yes, there are other ways to get Planetary Aegis artifacts, but they are very hard to come by.