Is it permissible to obtain the 'aqiqah from kitchens that provide sheep and undertake the cooking, after informing them that it is for 'aqiqah in order to fulfill the conditions?

The Aqiqah is only valid if it is slaughtered specifically for that purpose. It must meet the same specifications as an Udhiyah (sacrificial animal). There is no impediment to entrusting a kitchen owner or another person to slaughter and prepare it, provided the conditions are met. However, purchasing the meat after it has been slaughtered is not valid.