'se faire avoir' = 'to get oneself had', and that's 'had' in the sense of 'tricked' or 'fooled'. The Lawless French article on the 'reflexive causative' construction in fact includes the example 'tu te fais toujours avoir' ('you're always getting fooled'). See further at https://www.lawlessfrench.com/grammar/faire-reflexive-causative/

Just to add to Tom’s answer, ‘se faire avoir’ is a verbal expression, and of course ‘quand même’ is a very frequently used adverbial expression in French. ‘Quand même’ is one of those adverbs that seems to me to move a bit in everyday speech, but placement directly after the conjugated verb as here is quite ‘normal’.

In general it is better (or at least simpler) to accept expressions as they are - being expressions, they often carry meaning beyond or different to the sum of the individual parts. 

https://www.wordreference.com/fren/quand%20même  

https://www.wordreference.com/fren/se%20faire%20avoir

Thanks Tom and Maarten for your responses!  Very helpful!