Is it possible filing taxes on paper reduces the chances of being flagged for an audit?

Nope

Majority of audits are on paper returns

The IRS maintains that filing returns electronically can prevent mistakes and lower the odds of an audit. The error rate for a paper return is 21%. The error rate for returns filed electronically is 0.5%.

no................................................................

Let me assure you, ALL tax forms are electronically accessible.  Armies of clerks retype the ones that won't scan and be converted by an optical reader (eg, handwritten). The items that are PDFs are copies of receipts, documents, attachments and letters.  If tax data is on those forms, it is copied over.  If the clerks think something looks odd, they even have a "funny box" to put the paperwork in so another, more experienced, person will look at it.

You might slow the IRS down a bit by filing by mail, but the IRS does multiple passes of the data looking for issues.   They catch some issues when you efile (I had one catch a typo on an EIN number not matching the payer's name), others when they do the initial process and even more 18 months (or more!) when the IRS does matching and cross-year checking.  

Trying to game the system by filing a handwritten form by mail and late just doesn't work.

No, it makes no difference.

Don't lie and you won't be audited.

No.  The first thing the IRS does is scan the paper forms into electronic form.  Filing on paper may DELAY an audit, but will not ultimately reduce the audit probability.