Is balance sheet the part of accounting's double entry system?

No, not at all.
Balance sheet is not the part of accounting double entry system rather than it is a report or statement that shows the details of total assets, liabilities and capital of an entity at particular date.

The double entry accounting system mainly ensures that each transaction affects two ledgers.
These two ledgers could be Income/Expense accounts or Balance Sheet accounts.
There is no rule that each entry must affect both P&L and Balance Sheet.
Thus, to answer your question, Yes Balance Sheet (accounts) are also a part of the double entry system, however it is not mandatory to have a balance sheet account in each and every double entry transaction.
Hope to have helped clarify your doubts with my answer.

Is balance sheet the part of accounting's double entry system?

 

Actually balance sheet is depending on accounting's double entry system, therefore it is a part of accounting's double entry system.