1- your create a key palr (priv key, publc key) that also yields a non vanity bitcoin address, for example on electrum, preferably more secure on your own system.
2- upload the request for a vanity address and the public key to this pool or another service that has the processing power.
3- retreive the priv key from this pool. The actual address generation routine only uses public keys.
combine this priv key(unsecure) with your priv key(secure) to generate a new priv key(secure).
(an online utitlity to do this is here gobittest(dot)appspot(dot)com/VanityAll
but since it is on the internet it is less secure than running the keyconv util)
this new priv key gives you the vanity address.