If it reads wrong to you then I'd probably avoid using them, but in some situations it could work - if used correctly.
EDIT: Welcome to the SFF Crons, 11Comandment.
Quick google search and pulled this off a post
where somebody asked the same question:
| -- Are double semicolons; used thusly (albeit incorrectly); acceptable? |
You generally only use multiple semicolons when listing things and the use of a comma would be confusing:
Attending was George W. Bush, the president of the US; Tony Blair, the prime minister of the UK; and Saddam Hussein, the president of Iraq.
Otherwise, if you need to use double semicolons, there is probably something wrong with your sentence contruction. It's not grammatically incorrect, but it's stylistically awkward.