I just got contracted onto a film that starts shooting in October. The producers have asked me to get in touch with some brands to get sponsorship or gratis (credit in exchange for product.) I'm not really sure how to go about this. I have contacted a few companies but I have no idea who to reach out to or what to say.

Normally on set I use my own kit or kit provided for me.

Thank you in advance for any advice/answers!

Getting sponsorships can be difficult at best. The one underlying rule is that you have to make a reasonable request. For example a company that's well established isn't likely going to be interested in a small indie movie and a company that's just starting out may not have the ability to supply you with enough product for a large feature film. Additionally, you need to be in a position to offer something that the company wants and/or needs that they cannot get on their own. I'm not sure how much power you've been given by the producers but note that offering credit in exchange for goods is a proposition that many companies likely won't take, and with good reason considering that with the exception of people in the industry or looking to be in the industry it's not exactly standard for people to take note of what make-up was used etc in a film.

My advice to you is to be cautious about how you proceed, it seems odd to me that in lieu of being paid a kit fee or given a kit to use that you're being tasked with getting sponsors and donated products. As the point person (even if you have zero actual control) you're going to be the one who's screwed if the producers of the movie don't uphold their end of the bargain because you're the one making contact and making the deals. Your name and reputation could be seriously damaged if the movie doesn't come out, is distributed differently than expressed or if the credits aren't correct.

Agree.....

Think about protecting yourself - there are plenty of products & equipment that I won't use even if they were given to me for free.

And, as mentioned, what value will the company get out of a sponsorship?

I have been doing this for the past 8 years for my low budget films. I do offer media support  (FB, Twitter, Instagram) and my producers will always give screen credit (I ask the vendor how they would like to be credited).  It helps to have name actors though.

Make sure you approach the producers to ask them about film credit- if you say it's going to offset the makeup budget, they will always say yes.

I have production write a short synopsis about the movie starring the name actors, attach it to a letter to the vendor asking if they could "sponsor" the film with product. Generally they are agreeable (MAC is always awesome) and ask for a wish list and most of the time you get everything. I have it sent to me/makeup C/O the production office.

I have suffered no repercussions nor has it damaged my reputation. Even large budget films get sponsored with products (but the vendors usually have to give an insane amount of product, or the star must be amazing).

Normally someone from production handles this. You should ask to speak to someone in advertising and/or public relations. This is extremely unusual, I don't think I have ever heard of something similar. Is this perhaps a small independent production? They may not have much money and are trying to get as much as they can for free.