Hi Bill,
a layer 3 VXLAN gateway is used to route from one VXLAN to another, just as an SVI is used to route from one VLAN to another. The S-Series can be used as layer 3 VXLAN gateway. See
https://community.extremenetworks.com/extreme/topics/s-series-vxlan-lab-setup. It is independent of the underlay network if you need a layer 3 VXLAN gateway or not.
The VTEPs need to know each other for head-end replication of MAC address info. This can be achieved by manual configuration, or using the OSPF VXLAN extensions on Extreme switches.
The opaque LSAs used for Extreme's OSPF VXLAN extensions need to reach each switch with a VTEP. That should work by LSA flooding even for switches/routers that do not understand the contents of the opaque LSAs. If you need to add VTEPs on switches outside the OSPF domain, you need to use manual configuration for those.
VXLAN is a layer 2 tunneling mechanism (overlay) using a layer 3 interconnect (underlay). The layer 3 interconnect does not need to know anything about VXLAN in general.
You should consider using jumbo frames with adjusted IP MTU on the layer 3 interconnect to handle the VXLAN overhead.
HTH,
Erik