How could I block "Twitter’s Promoted Tweets"? I use the official iOS client. I also use the official OS X client, but so far didn't notice on OS X "Promoted Tweets".
Is the solution to switch to other iOS client? Which one without ads?
Twitter is injecting the promoted tweets into the stream. It's only a matter of time until they lean on every third-party app provider to stop filtering out the promoted tweets as this is how they're going to pay for the service.
In the short-term you can use a different client but in the long term all signs point to you being forced to see promoted tweets promoted tweets or leave Twitter.