Does Filing 1099 R Online with Form1099online.com secure?

Yes, it is secure as far as you get a secure IRS-approved e-file provider.
Also, online filing 1099 information returns are submitted to the IRS immediately, thus it consumes less time compared to the manual filing. You can register for free with an IRS-approved e-file provider & pay the processing fee to submit 1099 Forms online to the IRS.