oven alternatives

You could put a BBQ grill over one of the hobs (raised up if possible), then cook it over the "open fire". Frequent rotation and quite a bit of time may be needed to cook it suitably.

I have a fire pit and a grill when cooking outside over it - normally with God children round.

Use a Dutch oven.

Though this obviously assumes you own a Dutch oven or have access to one, there are still two additional things you'll need if you hope to succeed with burritos. The first is a good oven thermometer. The other is plenty of aluminum foil.

You'll want to raise the interior temperature of the Dutch oven to whatever is required of the instructions. And then you'll need to adjust the flame down in such a way as to keep the temperature right there in that range. There's really no way to do this without an oven thermometer (because who owns the digital laser kind?).

The foil plays two roles. One is for crumpling, the other for wrapping. The latter is optional. The former is not. By loosely crumpling an adequate amount of foil and then layering the bottom of the Dutch oven, you will successfully raise the burrito(s) off the bottom surface and bring a form of convection properly into play. Otherwise you'll bring only radiant heat into play and risk overly browning one side of the food. You'll also make the food more difficult to remove if it's not elevated. Finally, if you cap the crumpled layer off with several folds of foil, this will serve as a miniature tray.

Since this kind of cooking requires reaching into a cramped but very hot enclosure, please proceed with the appropriate degree of caution.