VXLAN configuration between ESX and F5, how?

This should get you closer. There are a few prerequisites that you must confirm first.

• At least one of the interfaces on the F5 should be connected to the "leaf and spine" infrastructure the ESX servers reside on.

The document provided by Carl Brothers is a good starting point. I have modified the instructions to better suit your environment and to remove some extraneous configuration components that can make things confusing (e.g. VLAN definition).

To answer your questions:

• Yes the FDB database entries are mandatory. VxLAN VTEP (end points) must have a IP->MAC mapping of all the devices within the environment. This can be done dynamically using multicast or in your case, manually if using unicast.
• The ESX gateway should be the IP address of the ESX host

NOTE: I typically place each route domain in a separate partition. This is an optional step.

create net tunnels vxlan vxlan-static {  
    flooding-type none  
}  

create net tunnels tunnel vxlan5000 {  
    local-address 10.30.0.x  Use an IP address that is in the same subnet as the ESX server 
    remote-address any  
    profile vxlan-static  
    key 5503  
}  
create net route-domain 5503 {   Used 5503 but any value can be used  
    id 5503  
    vlans add { vxlan5503 }  
}  
create net self 10.30.0.x%5503/24 {  
    address 10.30.0.x%5503/24  Use an IP address in the same subnet as the ESX server
    vlan vxlan5503    
}  
modify net fdb tunnel vxlan5503 {  
    records add {  
        00:FF:0A:03:03:02 { endpoint 10.30.0.222 }   MAC ADDR of ESX VM  
        00:FF:0A:03:03:03 { endpoint 10.30.0.222 }   MAC ADDR of ESX VM
    }  
}  
create net arp 10.30.0.x%5503 {   IP address of ESX VM  
    mac-address 00:FF:0A:03:03:02   MAC ADDR of ESX VM  
}  
create net arp 10.30.0.x%5503 {   IP address of ESX VM  
    mac-address 00:FF:0A:03:03:03   MAC ADDR of ESX VM  
}  

To validate that the tunnel is up and running and to view statistics, run the following command:

tmsh show net tunnels tunnel