I'd probably go for the raise as well since he's probably folding to any check-raise if he doesn't have the J -  but would fold to the shove since you then can be pretty sure that he has jx or better which would only give you 36% winning chance. If you had two overs to the board you should be calling a shove, but not with two middles. 

hope it helps a little

i think you can only answer the question if you think the hand through.

what will you do if villain calls your XR and your flush doesn´t come in? will you barrel turn AND river?

will villain only shove over your raise with Jx and better? do you think you will ONLY get called by Jx and better if you XR shove? i strongly doubt either. you´ll often get called by hands that you dominate, like some 3x and 4x, also 56 and 52 with a FD will always call you, also 3s2s will always call here. i think you avoid a lot of awkward situations on the turn and river if you just XR shove here. even against AJ you have 40% equity. add some fold equity from all the air that villain will lay down and XR all in becomes highly profitable.

i´d much rather XR NAI with a KJ or as a total bluff. by XR NAI in this situation, you will often get called by hands that right now are behind, but will be ahead OTT if your flush won´t arrive, like KQ, which is getting supreme odds to float you here.

if villain doesn´t have anything, like 96o, he will fold anyway, no matter if you raise all in or NAI. but if he does have something, even if it´s just K3o, you will get it in while ahead. and if he folds K3 to a shove, you´re not that unhappy either.

imagine the following: you raise NAI, villain calls with K3. the turn is the Kh, you bet 60% pot and villain shoves. that´s worst case scenario, you´re way behind but against his entire range you almost have the odds to call here. so which is better? getting it in with 50% on the flop or with 15% on the turn?

also: giving up your equity by raise folding here is just super bad. what if villain overprotects A4 here? what if villain shoves 3s2s, which is the right play with that hand, against which you have 50% equity? by raising NAI with the intention of folding to a shove, you´re making yourself highly exploitable.
 

cheers

s.

Standard check shove for me at this stack depth for most of the same reasons Dipl.komp has already stated.  Check raising 40 to 90 here just gives villain odds to float you with 2 overs which will hit 13% of the time which will just fold to a check shove, he can also take the play away from you on later streets if you miss.  

By check shoving he can also call you with 3 and 4 x which you are a favorite vs that you want him to commit all his chips with.  Factor that in with all the fold equity and the equity you have if called no other play is going be more profitable.  

To balance it you can just start check shoving vulnerable top pairs on wet boards at the same stack depth so that play isn't always a draw, if he knows you check shove draws it may get you some lighter calls the times you do check shove top pair by some weaker hands and pairs which he would normally fold which works out great for you.