In the beginning of Deathly Hollows Part 1, why didn't Harry or the others just teleport Harry instead of flying with brooms?
This was addressed in the source novel; Harry Potter and the Deathly Hallows. The Ministry of Magic has been thoroughly infiltrated. Since Harry Potter still has the Ministry's Trace on him (basically a magical charm that detects if magic is being used around an underage wizard), if they attempt to apparate him (or if he attempts to apparate himself), Voldemort's Death Eaters will be informed of it and will be able to abduct him with ease.
‘We are at an advantage there, my Lord,’ said Yaxley, who seemed determined to receive some portion of approval. ‘We now have several people planted within the Department of Magical Transport. If Potter Apparates or uses the Floo Network, we shall know immediately.’
‘He will not do either,’ said Snape. ‘The Order is eschewing any form of transport that is controlled or regulated by the Ministry; they mistrust everything to do with the place.’
There's also the fact that apparating in the vicinity of Harry Potter's house has been made illegal.
‘Pius Thicknesse has gone over, which gives us a big problem. He’s made it an imprisonable offense to connect this house to the Floo Network, place a Portkey here, or Apparate in or out.’
Taking him in this fashion would result in all of the Order members present being complicit in a crime. Since several of them are still in positions of power and influence, this would be unwise.
Because the Trace is still active on Harry and is used to detect magic casted around him, wherever he is. Apparition requires this kind of magic.
Moreover, the chimney network is not connected to 4 Privet Drive, so flying is the last viable option.
All of this is mentioned in Chapter Four: The Seven Potters