You're attempting to ask the driver to replace a fragment of a parameter with your argument. That's not the way it works. It doesn't want to look inside quotes for your parameters. Try instead:

my $query="SELECT * FROM tblBlogPosts WHERE fldTags LIKE ? ORDER BY fl
+dDate DESC";
my $sth = $dbh->prepare($query);
$sth->bind_param(1, '%'.$blogTagToShow.'%');
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Note: I'm basing this on how it works with SQL Server. I've never tried SQLite, so the rules may be different, and I may be talking through my hat.