No, you cannot transfer American Express Membership Rewards points directly to Southwest Airlines Rapid Rewards because Southwest is not one of Amex’s transfer partners.
There is an indirect transfer option of transferring Amex points to Marriott at 1 to 1 ratio and then transferring Marriott points to Southwest at a 3 to 1 ratio, but it’s a horrible deal. For example, 30,000 Amex Membership Rewards would convert to 30,000 Marriott Bonvoy points, which would only convert to 10,000 Southwest Rapid Rewards.
The better option is to transfer Chase Ultimate Rewards to Southwest Rapid Rewards at a 1 to 1 ratio from these cards:
American Express Transfer Partners
Here are American Express’ transfer partners that offer more value than the indirect transfer from Amex to Marriott to Southwest:
Membership Rewards Transfer Partners [1 to 1]
Aer Lingus Avios
AeroMexico [1 to 1.6]
Air Canada Aeroplan
Air France/KLM Flying Blue
British Airways Avios
Cathay Pacific Asia Miles
El Al [1,000 to 20]
JetBlue [250 to 200]
Hilton Honors [1 to 2]