Following the written rules for crafting magical items, you can imbue one of your pieces of armor with the spell Fly, or some variant (e.g. allow it to be cast multiple times a day). Note, however, that this will be extremely time-consuming, incredibly difficult, and excessively expensive. A piece of armor that provides magical protection, AC, and lets you cast Fly even once per day would be either Very Rare or Legendary (or Wondrous, depending) in my opinion.
For the specific requirements on that, I'd refer you to this excellent answer by David Coffron covering the exact requirements for crafting a new magical item. To summarize the time and money costs of creating enchanted items based on the Dungeon Master's Guide:
| Rarity |
Cost |
Minimum Level |
| Common |
100 gp |
3 |
| Uncommon |
500 gp |
3 |
| Rare |
5,000 gp |
6 |
| Very Rare |
50,000 gp |
11 |
| Legendary |
500,000 gp |
17 |
and Xanathar's Guide to Everything:
| Rarity |
Challenge Rating |
Time |
Cost |
| Common |
1 - 3 |
1 work week |
50 gp |
| Uncommon |
4 - 8 |
2 work weeks |
200 gp |
| Rare |
9 - 12 |
10 work weeks |
2,000 gp |
| Very Rare |
13 - 18 |
25 work weeks |
20,000 gp |
| Legendary |
19+ |
50 work weeks |
100,000 gp |
As you can see, regardless of the system, we're talking a cost of around a year of downtime effort, somewhere between 100,000 to 500,000 gold, and a very high level/DC for any hope at success.
Given the difficulty, this is probably not the easiest or quickest solution, but would be a very effective and reliable one, given enough time... and certainly a reasonable option given the value of what it is you are trying to create. Talk to DM about this and see if you can find a reasonable cost table you can both agree upon.