There's no evidence that they did.
The Tumblr post in question was published on 5 December 2014, according to a
<script> tag on the page. Since there's no time zone, I don't know exactly when the post was published or which span of time "tonight" refers to. Around that date, though, there were protests in New York City (and elsewhere in the country) over the death of Eric Garner (specifically, that a grand jury decided not to indict the cop who killed him). I searched on Google for the term "ambulance" along with relevant keywords, and I looked at several news reports of the protests, but I didn't see any claims beyond the Tumblr post that ambulances were used to transport police supplies.
Most reports don't mention ambulances at all:
- Balker, A., & Goodman, J. D. (2014, December 3). Wave of protests after grand jury doesn't indict officer in Eric Garner chokehold case. The New York Times. Retrieved from https://nyti.ms/2jD5C4l
- Southall, A. (2014, December 4). Protesters fill streets across U.S. over decision in Garner case. The New York Times. Retrieved from https://nyti.ms/1yYaPnZ
- —. (2014, December 5). Protests continue in New York City on Friday. The New York Times. Retrieved from https://nyti.ms/1u1qhcG
- MacMillan, R., Chung, A., & Malo, S. (2014, December 5). New York sees third night of protests over police violence. HuffPost. Retrieved from https://www.huffingtonpost.com/2014/12/05/new-york-protests-police_n_6279218.html
One article mentions that "The demonstrators congested city streets while traveling to their new rendezvous, only parting for an ambulance that needed to race through", but there's no indication that the ambulance wasn't actually responding to a medical emergency, nor that police took supplies from it: