If a creature that grants Regenerate with a static ability, like Heart Tree or Xrath, Dreadknight of Varna, is on the field when Zombie Dreadknight is played, the Dreadknight will receive the buff from its own ability. Static abilities are applied immediately so Dreadknight would have Regenerate as soon as it is in play. When the Forge trigger resolves, it would see that Dreadknight has Regenereate and give it the buff.
The interaction is different for creatures that grant Regenerate with a triggered ability, like Abyssal Brute. If Brute is in play and Zombie Dreadknight is played in a side space, both of their abilities are triggered at the same time and both get put into the same batch for resolution. The order in which they resolve is random. If Brute's ability resolves first, then Dreadknight will have Regenerate and receive the buff from its own ability. If Dreadknight's ability resolves first, it won't get the additional buff.