How are the amendments in the Bill of Rights denied to the citizens in the society in The Giver?

The citizens of Jonas’s society do not have any personal freedoms.  All of the decisions are made for them.  Therefore, their society has nothing similar to the Bill of Rights.  There are only strict rules and harsh punishments for not following them. 
The Bill of Rights is the first ten amendments to the United States Constitution.   The first one allows for free speech and freedom of religion, both of which are completely absent in Jonas’s society.  There are rituals, but they are secular and there is no mention of any kind of gods.  Free speech would be unheard of.  This is a society where it is expected that you will apologize of you offend anyone. 
There are also no books.  The only books in Jonas’s society are instruction manuals, so there is no press.  There are no magazines or newspapers.  Therefore, there is no freedom of the press since there is no press.  Jonas is shocked when he sees books in the Receiver of Memory Annex.  That is the only place they are. 

But the most conspicuous difference was the books. In his own dwelling, there were the necessary reference volumes that each household contained: a dictionary, and the thick community volume which contained descriptions of every office, factory, building, and committee. And the Book of Rules, of course. (Ch. 10) 

There is no mention of guns in the community, but if there were guns, citizens would not likely have them.  The community uses lethal injection to kill people, not guns.  Ordinary citizens are not allowed access to that either.  They have to request release to kill themselves.  A citizen who breaks a serious rule or three minor ones will be released, and citizens are released when they are deemed too old. 
As for Amendments Three and Four, there is no mention of a military, although the community does have search planes.  The citizens do not own their houses, because they do not own anything, so the community could quarter soldiers anywhere it wanted if it did have them.  There is zero privacy for citizens.  They have speakers where they allow the community elders into their homes at any time. 
As for the Fifth Amendment, which we usually interpret to mean that Americans do not have to incriminate themselves by testifying in court, I doubt that is the case in Jonas’s society.  When a citizen is accused of something they most likely have a video of it anyway, since it is very much a surveillance state.  Descriptions of the justice system make it seem very one-sided.  Jonas’s mother describes the justice system from her perspective as a judge. 

Today a repeat offender had been brought before her, someone who had broken the rules before. Someone who she hoped had been adequately and fairly punished, and who had been restored to his place: to his job, his home, his family unit. To see him brought before her a second time caused her overwhelming feelings of frustration and anger. (Ch. 1) 

The Fifth Amendment also includes a prohibition against double jeopardy, meaning that a person can’t be tried twice for the same crime.  Since justice is so harsh in Jonas’s community and people are pretty much just released, there is really no risk of that. 
However, they definitely get the speedy trial promised by the Sixth Amendment, if you can interpret it as a trial.  As for the Sixth, Seventh, and Eighth Amendments, Jonas’s community has no juries or bail (there is no money).  For the Ninth and Tenth Amendments, people have no real rights anyway, and there are no states so there are no states’ rights to worry about.
https://billofrightsinstitute.org/founding-documents/bill-of-rights/