According to Bulbapedia, the player can find Ho-Oh and Lugia on Navel Rock in Pokémon FireRed. Lugia is located on the lowest floor, and Ho-Oh is located on the highest floor. Upon encountering the Pokémon, the player can battle and capture them using Poké Balls.
Bulbapedia describes Navel Island as part of the Sevii Islands between Floe and Chrono Islands. To reach Navel Island in Pokémon FireRed, the player must obtain the Mystic Ticket through Mystery Gift, talk to the sailor in front of the Seagallop Ferries and sail to the island. Unlike the other Sevii Islands, Navel Island does not appear on the player's Town Map or PokéNav Map until the player reaches it. In Pokémon FireRed, the cave on Navel Island is silver.
The player can encounter Ho-Oh and Lugia on Navel Island. Lugia can be found on the lowest floor; Ho-Oh can be found on the highest, but it does not appear at first. Instead, it flies down and lands on a rock upon the player's arrival. Ho-Oh and Lugia both appear at Level 70. With high-level Pokémon, the player can battle Ho-Oh and Lugia and either knock them out or capture them. The Pokémon can also be found in Pokémon LeafGreen and Pokémon Emerald.