Can I share charge pumps between multiple L6206 H-Bridge drivers?
Yes.

ST has an application note document AN1762 for this circuit, which seems to be a good read when designing something with it. It has this chapter that seems to be really interesting to you.


  3.7 Sharing the Charge Pump Circuitry
  
  If more than one device is used in the application, it's possible to use the charge pump from one L6205, L6206
  or L6207 to supply the \$V_{BOOT}\$ pins of several ICs. The unused \$CP\$ pins on the slaved devices are left unconnected, as shown in Figure 10. A 100nF capacitor (C8) should be connected to the \$V_{BOOT}\$ pin of each device.
  Supply voltage pins (\$V_S\$) of the devices sharing the charge pump must be connected together.
  
  The higher the number of devices sharing the same charge pump, the lower will be the differential voltage available for gate drive (\$V_{BOOT} - V_S\$), causing a higher \$R_{DS(ON)}\$ for the high side DMOS, so higher dissipating power. In this case it's recommended to omit the resistor on the \$CP\$ pin, obtaining a higher current capability of the charge pump circuitry. 
  
  Better performance can also be obtained using a 33nF capacitor for C5 and using schottky diodes (for example BAT47 are recommended). 
  
  Sharing the same charge pump circuitry for more than 3÷4 devices is not recommended, since it will reduce the \$V_{BOOT}\$ voltage increasing the high-side MOS on-resistance and thus power dissipation.