Suggestion fuel

A common criticism of stage hypnosis (by those who don't understand hypnosis) is that the subjects are motivated to respond to the suggestions by the fact that they are in a situation where they are socially expected to comply and socially excused from the embarrassment. The hypnosis is real and there is a lot more going on, but that is important. Whether you are using hypnosis for party tricks, therapy, or anything else - motivation matters. Accepting a suggestion requires cognitive effort, and if there is no reason to do it, the subject won't. If there are additional reasons for them to not respond, then you need to overcome those as well before you can move on. Suggestions need their fuel.

I haven't seen this concept explicitly discussed in depth before, but hypnotists are certainly aware of it. There are a number of different sources of motivation that hypnotists use to fuel their suggestions and get the results they want from their subjects.

Leverage rapport.

• If we're having a conversation, you have something invested in the interaction. I can get you to say words to me by saying words to you. If you've gotten into a good rapport, then you can leverage that to get started - basically "Do this because I asked you to and you'd rather comply and keep this going than break rapport". Of course, this means that Omegle hypnosis is much harder if you don't spend time to develop a solid conversation prior to bringing up mind games. If you bring it up immediately, they have zero initial investment and therefore no reason to be engaged.
• You can escalate compliance by using simple 'yes ladders' (yay commitment and consistency!) and take this further, but you'll still end up limited to the force of "do it because I say so" (which can be significant).
• Use the unilaterally awkward silence. It won't take long for them to want to break it.

Control the frame

• Place responsibility on the subject so that success looks like they have a skill, and not like they're easily manipulated (which is the truth!)
• Have them do it because its exciting! Just watch out that you don't fall into a role as their jester, because that is lower status and you will lose the force of "because I say so".
• Offer them hypnocrack: "...and it feels good to do so"

Leverage large external pressures.

Prime them. Prime them hard. Hypnosis in therapy can be easier because responding to hypnosis can fix their problem - especially when you can put them up against the fear of not getting better if they don't find a way to make it work. This is much more important for real uses (and less important as a party trick).

A really fun way to leverage external pressure is to shove them between a rock and a hard place, and then suggest a way out. For example, if someone wants to fly but is phobic of airplanes, take their money and then force them to choose before the session whether they want to leave saying "It's good to be afraid of planes!" or to buy the damn ticket and board no matter what their fear level. Once they've bought the ticket, they'll be much more motivated to buy into your "it can be easy" frame when you offer it up.

Leverage hallucinated pressures. 

Have them hallucinate a scenario where there are external pressures. You're not going to get the same magnitude of response as if it were really happening, of course, but it can be very useful.

It's easier to have your suggestions accepted if you take the time to make sure that your subjects are motivated to respond to them.