Ok, ive done something like this before.
What you can do is the following....
52 cards in a deck. Obviously this would be 5 card stud. So there would be no need for a flor turn and river.
Each week you generally do 5 contests. Each contest winner received 2 cards.
At the end of each month, give 5 cards to the trivia winner, 3 to 2nd, 1 to 3rd, as its a longest contest.
Also - award a bonus card to people who maybe got insanely close to the arcade score, or asked a great question in 20 questions.
So.....
1 month.
Trivia Winner - 5 Cards. 2nd - 3 Cards. 3rd - 1 Card.
Contest Winner - 2 Cards.
Bonus Awards - 1 Card.
For the card drawing - use RANDOM.ORG - Playing Card Shuffler
This allows you to remove the cards a certain player already has! Obviously you PM the cards to the winner, and it is up to them to make the winning hand in the claim period after the events.
The issue with drawing a flop is it would mean someone with only 1 card could have the nut flush, while someone who has won 10 games, would only be able to maybe have trips or something as they didnt get the Ace of spades.