The level gained with Delta Flyer's effect is permanent as long as the monster remains face-up on the field.
Since Delta Flyer is a Dragon-type Tuner he fits perfectly in a Dragunity deck which has lots of Synchro monsters all requiring a Dragon-type Tuner. Delta Flyer's effect could then be used to adjust the other Synchro material's level to the level you need for your Synchro summon.
Cyberdark monsters are able to use level 3 Dragons, like Delta Flyer, from your graveyard as equips to boost their own stats. Additionally, since most of the main deck Cyberdark monsters are level 4 monsters, you can use them alongside Delta Flyer to make level 7 and 8 Synchro monsters.
Greed Quasar and The Calculator both rely on increasing levels to gain attack. Delta Flyer can then be used to help these monsters by increasing their levels every turn which in turn boost their stats.
You can use Delta Flyer to turn a level 4 monster into level 5 which would give the monster an attack boost from Beatdown! and all monsters affected by Beatdown! will also gain an additional 300 attack.