There should be no impact on flights, even in the event of no deal. The European Commission just adopted some legislation yesterday to put in place "no deal" contingency plans in certain sectors, including in transport. This is from their press release:
"Transport
The Commission has today adopted two measures that will avoid full interruption of air traffic between the EU and the UK in the event of no deal. These measures will only ensure basic connectivity and in no means replicate the significant advantages of membership of the Single European Sky. This is subject to the UK conferring equivalent rights to EU air carriers, as well as the UK ensuring conditions of fair competition.
- A proposal for a Regulation to ensure temporarily (for 12 months) the provision of certain air services between the UK and the EU.
- A proposal for a Regulation to extend temporarily (for 9 months) the validity of certain aviation safety licences.
The Commission has also adopted a proposal for a Regulation to allow UK operators to temporarily (nine months) carry goods into the EU, provided the UK confers equivalent rights to EU road haulage operators and subject to fair competition conditions."
This should avoid any problems with flights operating into/out of the UK, as long as the UK is prepared to guarantee the same rights to EU carriers.
However, I would anticipate that their might be some big delays at the border, so I would plan extra time to check in and get through customs/arrivals at the UK end.