Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
Vinegar in Shari'ah
When a substance changes and becomes another substance, the ruling regarding it changes as well. Example, juice (Halal) becomes wine (Haram) then becomes vinegar (Halal). (Nurul Idhah Pg. 54, Hashiat Tahtawi Pg. 165)
Please also refer to: http://www.muftisays.com/qa.php?viewpage=viewQA&question=451
Therefore, it is permissible to consume vinegar made from wine as long as the origin and effects of alcohol, e.g. intoxication, are altered and transformed.
Narrated Jabir ibn Abdullah
Allah's Messenger (Sallallahu Alaihi Wasallam) asked his family for sauce. They (the members of his household) said: We have nothing with us but vinegar. He asked for it, he began to eat it, and then said: Vinegar is a good sauce, vinegar is a good sauce. (Muslim)
Note: The ruling about vinegar is general (Aam) in this Hadith, he did not exclude any type of vinegar.
Prophet (Sallallahu Alaihi Wasallam) said: “The best of your vinegar is your wine vinegar.” (Sunan al-Bayhaqî, Nasbur Rayah)
(See also: I'laus Sunan Vol. 18 Pg. 43, Raddul Mukhtar Vol. 5 Pg. 320, Badai' Vol.5 Pg.113, Takmilah Fathul Mulhim Vol. 3 Pg. 612)
(Darse Tirmidhi Vol. 4 Pg.196,197)
And Only Allah Ta'ala Knows Best.