I'm not sure if you're requesting help on transferring to Section 8 housing in Brooklyn, a market rate rental apartment in Brooklyn or whether you're looking to purchase an apartment in Brooklyn. Unfortunately, I don't know much about the Section 8 process, but nyc.gov has a web site that might help you. Please see the link below.
If you're looking to move into a market-rate rental apartment or an apartment to purchase, you may want to speak to someone to make sure your participation in any other govt. subsidies aren't affected.
Landlords are looking for: good credit (so check your credit history), income and personal and/or professional references. When preparing to move to apply to a new apartment, it's a good idea to start getting this information together. Lenders and co-op boards are looking for essentially the same information, but in greater quantity and detail.
Hope this helps.