You asked if Jeremiah 3:16 was speaking
about this happening during the thousand year
kingdom. The answer to your question is yes.
Jeremiah 3:16, "And it shall come to pass, when ye be
multiplied and increased in the land, in those days, saith the LORD, they shall say no more, The ark of the covenant of the LORD: neither shall it come to mind: neither shall they remember it; neither shall they visit it; neither shall that be done any more." Jeremiah 3:17
answers your question because it says, "At that time they shall call Jerusalem the throne of the LORD; and all the nations shall be gathered unto it, to the name of the LORD, to Jerusalem: neither shall they walk any more after the imagination of their evil heart." This will happen
during the Lord Jesus' 1,000 year reign on
Earth.
In
answer to your question "Will the ark be found again, after
missing for 2600 years, since Nebuchadnezzar
came against Jerusalem?"
the answer is yes, the Ark of the
Covenant has been found according to the Temple
Institute and according to Ron Wyatt. At this
link
gallery - Temple
Institute click on the photo that says
'Ark of the Covenant' (not the photo that says 'Winged
Cherubim') This is a replica built by the Temple
Institute. This page says "The original ark, created
in the desert, lies hidden in a chamber beneath the
Temple Mount and will be revealed with the building of
the Holy Temple." (The Third Temple will be the
tribulation temple.)
There is also an Ark of the
Covenant in heaven according to Revelation
11:19. The Ark of the Covenant made in the
desert was a pattern of the Ark of the Covenant in
heaven along with the Tabernacle.
Hebrews 8:5, "Who serve unto the example and shadow of heavenly things, as Moses was admonished of God when he was about to make the tabernacle: for, See, saith he, that thou make all things according to the pattern shewed to thee in the mount."