Q: can I buy additional iCloud storage by using a family shared credit card?

Only the person who organized or set up the family sharing can purchase iCloud storage -- Family purchases and payments - Apple Support

That article says the iCloud upgrade will be billed to the family organizer.  I haven't tried it, but it seems the family member should upgrade their storage plan like it was them and the family organizer should be billed.  I haven't done this so OP can try it and see what happens or wait until someone who has tried it comes along an advises or contact Apple Support at https://www.apple.com/emea/support/icloud/contact/

When someone upgrades their iCloud Storage plan, the upgrade will be billed to the Apple ID that they use with iCloud. If they're in a family group and they use the same Apple ID in iCloud and iTunes, the upgrade will be billed to the family organizer.

I read it differently as this is the first paragraph --

"With Family Sharing, one adult in the family—the family organizer—agrees to pay for any iTunes, iBooks, and App Store purchases that other family members initiate while they're part of the family group. This also includes content that can't be shared with the family, such as ongoing subscription purchases initiated by family members, including iCloud storage, and iTunes Match subscriptions."

To me, all that paragraph says is that the Family Organizer cannot buy iCloud storage and share it with Family Members.  So OP can't buy a 50GB plan and let his son (assuming there is one) use that storage.  I think he can let his son purchase 50GB of iCloud storage, approve the purchase and be billed for his individual 50GB storage plan.