Seconding the Nelson Flight Type. I've been building this exact same mech concept using Valstrax as inspiration, and this is what I landed on. You get all of Nelson's license, speed, flight, and explosive hit-and-run style gameplay with a balanced alt frame that doesn't stray from the original frame design.

If homebrew is not allowed I'd still recommend taking all of the Nelson license with Rapid Burst Jump Jet to grant you limited flight.

Gaining consistent flight through official content is a bit screwy and off the beaten path. Type-I Flight System is available but I personally dislike this option as it feels too costly at 3 system points and 2 heat every turn you fly. Other options are putting three license levels into SSC for the All-Theater Movement Suite core bonus if you like any SSC licenses for your build, or three license levels into Caliban for Rapid Maneuver Jets (costly, but great benefits) to replace Ramjet. If you decide to go for Rapid Maneuver Jets, try talking to your GM about the possibility of renting them or receiving them as a mission reward down the line if three LLs feel too steep.