How do Anglicans, who recognize apostolic succession, trace theirs? It appears Anglicans claim apostolic succession.
How do they trace their apostolic succession?
The same way that the Catholics do.

Anglicans consider themselves catholic and reformed. The Anglican church was the Catholic Church in England until the reformation when they stopped recognizing the authority of the Pope. 


  "The roots of the Church of England go back to the time of the Roman
  Empire when Christianity entered the Roman province of Britain.
  Through the influences of St Alban, St Illtud, St Ninian, St Patrick
  and, later, St Augustine, St Aidan and St Cuthbert, the Church of
  England developed, acknowledging the authority of the Pope until the
  Reformation in the 16th century." (An Ancient Church, Catholic and Reformed - www.churchofengland.org)


They trace their apostolic succession through the bishops who were members of the historical episcopate that remained in England after the schism.