Whether Andy Reid accepts the job with the Chiefs or holds out for the Chargers, he is obviously going to want to bring some of his former assistants along with him. Marty Mornhinweg's contract is up, so he's free to go and is probably a good bet to be on Andy's staff in some capacity. Juan Castillo was obviously fired by Andy, so he could go.
Otherwise he'll have to get permission from the Eagles for any other coaches under contract. The team elected not to fire the staff along with Andy, with owner Jeff Lurie saying he wanted them to complete their end of season player evaluations and wanted to give them an opportunity to meet the new coach.
One of those guys wants to bring, according to Howard Eskin, is QB coach Doug Pederson and reportedly the Eagles will let Pederson out of his contract. We can also take this to mean that Andy has already begun to assemble his staff.
One guy they will not be allowing Andy to take is Duce Staley. Both Eskin and Ruben Frank have confirmed that higher ups in the organization really like Duce and have made it known that he will not be allowed to follow Andy.
Duce was drafted by the Eagles in 1997 and enjoyed a very success run with them until 2003, before heading to Pittsburgh as a free agent. Duce got pretty good money and a won himself a Super Bowl ring, but injuries prevented him from ever playing a meaningful role there. He played in just 16 games over 3 seasons.
Staley would return to retire as an Eagle in 2007 and signed on as a coaching intern in 2010. In 2011 he was officially given the title of special teams quality control coach, but his role has always been very general. He'll work with the RBs and other positions and could always be seen standing close to Reid, involved in discussions during games.