Google "Flat Fee MLS + your city" and you'll find plenty of websites that offer the service to place your home on the MLS as a FSBO (technically it's For Sale by Agent once it's listed on the MLS, even though all the agent is doing is listing it on the MLS.
Here are the big things to look for in a flat fee MLS listing:
1. The Listing must be on the Local MLS.
There are hundreds of MLSs in the United States. Sellers want to be on the MLS that covers the area where their home is located, so the local buyer agents can see the home when they log into their MLS (and can see the commission offer).
Note that if the local MLS is very small or very expensive to join, you may not be able to find a broker that offers flat fee listings. In that case you can consider using a neighboring MLS. Basically all MLS' syndicate to websites such as Redfin, Zillow, realtor.com, and broker sites.
2. Cost to List + Changes to Listing.
A listing can cost from ~$100-$400. Watch out for fine print that requires an additional fee at closing or takes a portion of commission from the buyer agent - this is a big red flag.
Make sure you are able to make changes to the listing after it has been posted for a nominal fee. Most sellers use ~5-6 changes. Note that a change can be anything such as pictures, description, price and status. Some services may offer a low listing fee (e.g. $100), but then charge $25+ per change.
3. Photos on MLS.
Make sure you can upload at least 12 photos. Some services offer a great price, but it's only for 1 photo - which is not useful for most properties. Home buyers are very easily visually influenced. Pictures work wonders and numerous studies have shown that pro photography pays for itself many times over.
4. Length of Listing.
Get at least a 6 month listing and be sure that there is no charge for cancellation.
5. Fine Print.
You should never be required to use any closing service (e.g. escrow) provided by the flat fee service agent. Read the listing agreement carefully - you will be required to sign one in every state.
6. Be Careful With Referral Services
Many of the flat fee MLS listing service providers you come across on the internet are actually just middlemen. These referral services find flat fee agents in each state and then advertise flat fee MLS listing service to sellers. These referral services have you add property info, photos, etc. but then send your info to the listing agent who does the work (and gets paid by the referral service).
Here's the catch: The actual listing agent is going to need to send you the real listing input form for your local MLS. The generic form that the referral service had you fill out is basically useless. Check out the listing input forms for a residential property for two different MLSs: Los Angeles and San Diego (in case you want to see how different the forms can be). Note that many fields are required on the forms and typically only the seller is going to know the right info.
You will be required by state law to sign a listing agreement with the listing agent. It can be very dangerous paying for a listing without knowing what terms you are going to be required to agree to.
To recap: Be extremely cautious with flat fee MLS sites that only refer business to other agents.
Bonus Points
You should also consider the ease of use of the flat fee MLS listing provider, for example, can you complete everything online? How quickly is the listing added to the MLS? How quickly can changes be made? Is the agent easy to get in contact with?