I think goldmandra has hit the nail on the head with the causes of this behaviour, she is confused and insecure, getting mixed messages, although I think there are things you and your dh can do before going to find external help.
When she is doing chores make sure you praise her for doing it well, that way she will have more self respect and feel good about herself, and about you, and who knows you -may be able to get her to help more often.
If you have a little one as well then perhaps the older one is growing up more quickly than some other posts daughters, and perhaps she would welcome being treated as responsible member of the household who has something to contribute. Plenty of praise is needed, catch her being good rather than noticing the bad too much.
She is getting bored - you need to give her something to do - get her to help you or your dh with the chores regularly - give her some responsibilty , pick something she might enjoy and is able to do at least after some practice. Make her feel good by praising her when she does it well, make it an opportunity for you to chat about girly things together. Washing up with you or emptying the dishwasher?
Perhaps you could leave the other 4 with dh for a day and take her shopping and chat with her to make sure she knows you love her and make her feel special. I find this works a treat with my 13 year old when she starts to play up. Also might help dh realise how much work they are!
I dont think you can take away the instagram permanently now she is used to it, but there can still be boundaries, for example no phone after 8pm in term time. Rewards for good behaviour and/or helping with housework - chocolate, money, more credit on the phone, trip to macdonalds, whatever it takes - more effective than punishments imho.
Most importantly, you need to be on same wavelength as dh. If he is letting you try your method for a week this wont work unless he is also buying in. If he does not agree with and support your method you may have to consider trying his method and use carrot and stick, positive messages for positive behaviour whilst also consistent boundaries. Compromise I know and I do think he is being a bit useless but it is really really important you both are consistent, perhaps more important than which method you use.