It's impossible to say when, or indeed whether, any deportations under this plan will take place.
Currently, the plan has been blocked by an interim measure granted by the European Court of Human Rights in the case of N.S.K. v. the United Kingdom, which directed the Government to wait until three weeks after the conclusion of the domestic judicial review process to deport the applicant to Rwanda. Once this measure was granted, the other potential deportees also filed similar appeals, and the Government was forced to drop their removal orders for the time being.
The High Court is apparently preparing to deliver its judgement on the aforementioned judicial review imminently - but whatever the result, it's likely that the case will be sent to the Supreme Court on appeal.
Even if the Government is successful in this review, and the court's judgement is not appealed, the timeframe for the departure of the first group of asylum seekers is unclear. Omar Daair, the British High Commissioner to Rwanda was asked just this question at a press conference on Wednesday:
I can't yet fully predict the timeline of when that might be, until we are informed of the verdict on Monday.
Of course, Parliament also remains sovereign, and could pass primary legislation to overrule the courts or withdraw from the ECHR altogether, meaning flights could begin immediately.