Are there PCB connectors capable of suporting more than 3.5kV of working voltage?
It's not only the dielectric strength that you must worry about, but also the spacing between connectors. As you know, high voltage tends to arc. Because of this, you won't find connectors that are closely spaced in high voltage parts, even with high dielectric strength materials, per IPC spec, there is a minimun distance even if there is insulation. 

If you want to find addtional distances that are not on the table, then use the calculator. 
At 6kV, the minimum distance is 30mm if you have bare conductors, and 18 for coated/insulated conductors. 

For example:
At 40kV this distance increases to 200mm and 121mm (coated). For this reason it would probably be rare to see connectors with two conductors as the conductors need to be placed 121mm apart per IPC spec. The traces on the board would need to be 100mm apart. 

The clearance calculation does not account for the dielectric because the IPC spec only considers coated vs uncoated conductors. The spacing needs to be the same no matter what the dielectric breakdown is. In addition to that, the terminals pictured above have bare conductors, and this needs to be taken into account in the clearance calculations. 


Source: http://www.smpspowersupply.com/ipc2221pcbclearance.html


  How can I do this? How can I put connectors with this voltage of
  difference between one connector and the other one?


After determining the max voltage, then deterimine how far apart the connectors need to be and get connectors that are single terminal, not multi terminal and space them the required distance apart.