Heads and tails are the two sides of a coin. "Head" is also a slang term for being fellated, and "tail" is a slang term for female genitalia. By "getting head" and "needing tail" the rapper both receives oral sex and desires to fornicate.
"Birds" and by extension, "chickens" are urban slang for kilograms of cocaine. Our rapper here is claiming that buy distributing a kilogram of cocaine, or "crossing the street" with it, he earned eighteen thousand dollars.
A "package" is urban slang for a delivery of drugs. His "whip game proper" means that he knows to use inconspicuous cars at legal speeds to not alert the attention of authorities when delivering said drugs via automobile.