Well since a Wind Style: Rasengan wraps the opponent in a tornado of microscopic cutting wind and a Fire Style: Rasengan causes a massive amount of fire to engulf the opponent I think together the microscopic wind would power up the fire to a point in which it melts the opponent's flesh and it could possibly condense the fire into a smaller flame that's strength would be greatly increased
Fuuton: Rasengan (Wind Style: Spiral sphere)
Type:Attack
Rank: A
Range:Short
Chakra Cost:30
Damage Points:60
Description: Rasengan doesn't require handseals, only molding of the chakra. The user focuses and creates a fast, rotating sphere of chakra in the palm of their hand which can cause much destructive impact. A direct Rasengan hit can be lethal but the user needs to actually physically hit the opponent for it to work.
(Katon: Goen Rasengan) - Fire Style: Flame Rasengan
Rank: S
Type: Offense
Range: Short
Chakra Cost: 40
Damage Points: 80
Description: The user creates a normal Rasengan and covers it in flaming fire chakra. They then hit the opponent, causing a blazing maelstrom of fire, burning them and their surroundings.
BUT if you use a RasenShuriken I believe you would make a forbidden combo
(Katon: Goen Rasengan) - Fire Style: Flame Rasengan
Rank: S
Type: Offense
Range: Short
Chakra Cost: 40
Damage Points: 80
Description: The user creates a normal Rasengan and covers it in flaming fire chakra. They then hit the opponent, causing a blazing maelstrom of fire, burning them and their surroundings.
Fuuton: Rasen Shuriken (Wind Style: Spiraling Shuriken)
Type:Attack
Rank: S
Range:Short
Chakra Cost:40
Damage Points:80
Description: A combo of the rasengan and wind manipulation that encases the opponent in a huge violent orb of slicing wind that draws in anyone near by and cuts on the microscopic level but causes +10 damage to the user.