No one is asking for private information. Posting tx ID, signing a message using a bitcoin address is not private.
Blockchain is an open ledger which is public to everyone

To prove what? To who? Why and how that will help the case?
To prove that he is the one who deposit those coins?
That kind of stuff should be done only by request from the casino only if they needed.
Requested by randoms and the time wasting for providing it which will not affect anything is annoying time wasting.
Isnt the casino bad?
By providing evidence that he got scammed, people can tag Cloudbet and let others know that they may be scamming people. That would taint their reputation or maybe even make them come here answer OP.
If providing all this information for us, a bunch of randoms, is such a waste of time, then why the heck did OP even create this thread in the first place? Go eeal with the casino or with the police.
Now you can stop trolling, k?