Waw...
Fact: Printing of RGB color way different then printing converted from RGB to CMYK in any graphic software (Corel, Adobe etc.) through the (any color profile)
Step #1 Made the color swatch print for all type of materials you have to use in shop. Put the exact numbers of RGB and CMYK below each color square in swatch grid. This is the base should be in every print shop.
Step #2 If in the workflow, by some reasons, you use pretty long chain of software/color profiles/export operations, the best way to find at what point your color going wrong way start from the end of chain - RIP. In your particular case this chain is: Corel - PDF - Flexi - RasterLink. So you can rasterize the file after the Flexy in Photoshop (under generic Adobe RGB color profile) and check the color numbers of Red Color by Color Picker tool. Then you go to Color Swatch Grid you did in Step #1 and check how far you from color you need. If color wrong so go to check previous Exporting step. IN your case it is PDF. Rasterize PDF in Photoshop and repeat the Step #2. In case you find the victim software ...
Step #3 Let's imagine that your wrong working export is Corel... So now you can ask for more professional help from Corel professionals about: what color profile better use on PDF Export.