Can you get the flu vaccination after you have had the flu?

First, to be sure your question is fully answered and understood, the flu vaccinations are for prevention of infection with the exact type of flu that is contained in the vaccine, so if you have already been ill with the flu then there is no need to vaccinate to prevent that same flu, since your immune system will naturally develop immunity to future infections by that same virus from having had the flu without a vaccination.

But, since there are so many different types of flu viruses, and since usually no lab testing is done to determine or confirm the exact strain of virus that has made you ill, then you will still need to get the vaccination for the seasonal flu, which, in most locations of the world, will contain vaccine against the three most prevalent flu viruses circulating at that time. The vaccination will be still needed to protect you from any of those other flu viruses that you have not yet been exposed to.

So, to answer: Yes, you can get the flu vaccination after you have the flu unless you are not fully recovered and still have a fever. It will not hurt you to receive a vaccine for a virus that you have already been exposed to or that has already made you ill. Your immune system will just say, "Been there done that" and go to work on creating immunity to any other viruses in the vaccine that it has not seen before.