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16 badges. 8 from Jhoto and 8 from Kanto.
There is 16 badges in Soul Silver, both 8 in kanto and jotho.
You can access Cerulean Cave in SoulSilver after you get all 16 gym badges (Johto and Kanto).
In HeartGold and SoulSilver, yes, you will be able to go to Kanto and travel mostly its entire region which includes battling the Kanto Gym Leaders, but first the Elite Four. After, you've gotten all 8 Johto badges, talk to Prof. Elm and he'll give you a ticket to S.S. Aqua, which will take you to Kanto.
there is 16 badges... 8 in kanto and 8 in johto