Nidoqueen and Nidoking are two of the most powerful Pokemon to come out of Kanto and the first Generation.
While they have some slight differences, Nidoking and Nidoqueen have a ton of similarities. They are both incredibly strong and can utilize the same moveset in order to dominate in battle.
Nidoqueen is a bit more defensive than Nidoking, but it isn't enough to make a dent in the moveset they can share. As Poison/Ground-types, the two fully evolved Nido Pokemon are very dangerous.
The best moveset for Nidoqueen and Nidoking in Pokemon Red and Blue
Both Pokemon get a massive Same Type Attack Bonus when using Earthquake. That makes the move even more devastating than it already is. Earthquake does tons of damage and is one of the most powerful moves in the Pokemon universe. These two hard-hitting creatures will be able to use it well.
Blizzard is one of the most powerful moves to come out of Pokemon Red and Blue. Seriously, if there is a Pokemon on your team that can learn Blizzard, give it to them. In Generation I, it has a 90% Accuracy compared to a 70% in later Generations. It does massive Ice-type damage and has a 10% chance of freezing the opponent.
Thunder and Thunderbolt are both incredibly strong Electric-type moves. As part Ground-type, Nidoking and Nidoqueen can use an Electric move to deal damage to those that may cause it the most harm, like a Water-type. Both have a 10% chance of paralyzing the target. Thunder is less accurate and has more power. Thunderbolt has 100% Accuracy, but less power. It is truly up to the trainer.
Lastly, Body Slam gives it another type move that simply deals damage. It has a 30% chance of paralyzing any Pokemon that isn't a Normal-type. It is simply a finishing maneuver that can take out Pokemon that may resist some of the other moves in the set. With this, Nidoking and Nidoqueen have a well-rounded, dangerous moveset for Pokemon Red and Blue.