Not sure if the OP wants to learn slang exclusively..DR colloquial speech most likely
... the OP (original poster) has not returned and one time posters usually don't but...
I don't think the OP wants to learn Dominican slang per se. I think s/he wants to learn to speak the Dominican vernacular meaning the colloquial speech of Dominicans. The word slang is used very loosely by many who are not as informed about language but slang refers to words and/or short phrases or expressions that replace the more generic word and usually understood by a specific group of people and certainly coined by them. Some slang has become official words and can be found in some resources where as others are strictly limited to a specific social group or group of speakers but may not be considered official words (yet). People learn slang when they hear the words used in context and make the association as to what they refer to and when to use them if they choose to use slang for whatever reason. For example, the word money, common slang variations in English are 'dough', 'bread'. There are many slang equivalents in Spanish.
Slang however should not be confused with regionalisms. Regionalisms in Spanish refer to words that are not considered the standard but are used in certain regions and countries. They can be found in many references and usually when used by speakers identify where they are from or their influence in Spanish. Good examples are fruits and vegetables. There are many word variations in Spanish to refer to the same fruit or vegetable which can be at times confusing depending on how broad one's vocabulary is in Spanish. The more regional vocabulary you know the better in my opinion or ask the locals how XYZ is said to avoid confusion. Fruits in the Caribbean have similar words/ terms but the same fruit may be called something completely different in Central America. A good example is gand?l vs guand?l right in the Caribbean- same vegetable (pigeon peas) with a definite word variation. A classic example is the word 'calimete' meaning straw but in the Dominican Republic only. The variations for the word straw in the Spanish-speaking world are vast. It's best to learn the regional/ local word. However, in some countries you will hear what is considered the standard. Guagua and its varied meaning is another example of a regionalism in Spanish.
Colloquial speech is what I believe the OP wants to learn which can include slang, religionalisms and other vocabualry. Colloquial speech refers to the way Dominicans speak- sentence structure primarily thus dropping the /s/ everywhere, shortening words and over usage of the pronouns t? and usted are some features of Dominican colloquial speech that readily come to mind. A noted example is the OP's screen name. That's an example of colloquial speech although I think the OP has it reversed. That sentence formation and speech pattern is particular to Dominicans, the Caribbean and Caribbean basin regions. To learn to speak that way you would have to be around Dominicans who speak like this all time which is the vast majority. Dominican speech is very informal and the colloquial speech in my opinion is the standard. Other examples of colloquial speech are: the Dominican political slogan E' pa' lante que vamos or Elvis Crepo's ?chate pa 'ca, 'ta loco, pa' que sepa(s) etc. All these examples can also be Cuban or Puerto Rican colloquial speech or known as el habla popular in Spanish. It's very different from what you hear from other Spanish speakers and noted by them as well.
• In summary, slang you can learn from people who use a lot of substitute words and this vocabulary is often specific to a group of speakers, as well from songs (there's plenty of colloquial speech in merengue) and TV programs.
• Regionalisms are part of everyday words used in the DR or Caribbean but may not be used in other Spanish-speaking countries. You can learn regional words and to have a broad vocabulary in Spanish is an advantage in my opinion.
• Colloquial speech in this case refers to DR speech patterns (as defined above) which can include slang and regionalisms. This is harder to learn if you are not in the DR, around Dominican speakers on a regular basis or learn Spanish outside of the DR or Caribbean region. (of course if one chooses to speak this way)
It's not correct to use the umbrella term 'slang' to refer to these distinct linguistic concepts.
-MP.