I see this behavior in my dogs probably the most, where it wants to flaunt something it has, like a toy, in order to try and make me jealous. It's not just the ask for attention, but the behavior to try and incite an emotional response.
show-off [shoh-awf, -of] noun http://www.dictionary.com/browse/show--off?s=t
- a person given to pretentious display.
- the act of showing off.
note "pretentious" can mean "making an exaggerated outward show; ostentatious" and something "ostentatious" is "in order to impress others" or "intended to attract notice"
In many situations like this I might expect to see the term "taunt with", in the sense of "to taunt [someone] with [something]". There has been some difficulty finding a suitable definition to cite here, as most do not have this specific usage listed, but it is common where I live.
"taunt someone with something" -- to tease or tantalize someone with something. Jerry taunted Fran with the plate of fudge. Please don't taunt me with food I shouldn't eat.
I think if you just said "to provoke to jealousy" it would work. (Obviously not a single word as you requested but keep reading below...)
For example, this wording is in the ESV translation (and others) of the Greek New Testament. 1 Corinthians 10:22 "Shall we provoke the Lord to jealousy? Are we stronger than he?"
Interesting side note is that the ancient Greek had a single word for it: . Most English translations go with this multi-word translation of provoke to jealousy in 1 Corinthians and other places in the New Testament.
My dog tried to provoke me to jealousy through playing with the toy.