diff --git a/dask/array/core.py b/dask/array/core.py
--- a/dask/array/core.py
+++ b/dask/array/core.py
@@ -3977,7 +3977,8 @@ def concatenate(seq, axis=0, allow_unknown_chunksizes=False):
     ----------
     seq: list of dask.arrays
     axis: int
-        Dimension along which to align all of the arrays
+        Dimension along which to align all of the arrays. If axis is None,
+        arrays are flattened before use.
     allow_unknown_chunksizes: bool
         Allow unknown chunksizes, such as come from converting from dask
         dataframes.  Dask.array is unable to verify that chunks line up.  If
@@ -4015,6 +4016,10 @@ def concatenate(seq, axis=0, allow_unknown_chunksizes=False):
     if not seq:
         raise ValueError("Need array(s) to concatenate")
 
+    if axis is None:
+        seq = [a.flatten() for a in seq]
+        axis = 0
+
     seq_metas = [meta_from_array(s) for s in seq]
     _concatenate = concatenate_lookup.dispatch(
         type(max(seq_metas, key=lambda x: getattr(x, "__array_priority__", 0)))

diff --git a/dask/array/tests/test_array_core.py b/dask/array/tests/test_array_core.py
--- a/dask/array/tests/test_array_core.py
+++ b/dask/array/tests/test_array_core.py
@@ -577,6 +577,16 @@ def test_concatenate_unknown_axes():
     assert_eq(c_x, np.concatenate([a_df.values, b_df.values], axis=1))
 
 
+def test_concatenate_flatten():
+    x = np.array([1, 2])
+    y = np.array([[3, 4], [5, 6]])
+
+    a = da.from_array(x, chunks=(2,))
+    b = da.from_array(y, chunks=(2, 1))
+
+    assert_eq(np.concatenate([x, y], axis=None), da.concatenate([a, b], axis=None))
+
+
 def test_concatenate_rechunk():
     x = da.random.random((6, 6), chunks=(3, 3))
     y = da.random.random((6, 6), chunks=(2, 2))

`concatenate` inconsistency with NumPy for `axis=None`
**What happened**:

Calling `concatenate` with `axis=None` gives an error rather than flattening the inputs, which is what happens in NumPy.

**What you expected to happen**:

Behaviour the same as NumPy.

**Minimal Complete Verifiable Example**:

```python
>>> import numpy as np
>>> np.concatenate([np.array([1, 2]), np.array([[3, 4], [5, 6]])], axis=None)
array([1, 2, 3, 4, 5, 6])
>>> import dask.array as da
>>> da.concatenate([da.array([1, 2]), da.array([[3, 4], [5, 6]])], axis=None)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/Users/tom/projects-workspace/dask/dask/array/core.py", line 4050, in concatenate
    if axis < 0:
TypeError: '<' not supported between instances of 'NoneType' and 'int'
```

**Anything else we need to know?**:

This fix is needed for the Array API (https://github.com/dask/community/issues/109), where the function is called `concat`.

**Environment**:

- Dask version: main
- Python version: 3.8
- Operating System: Mac
- Install method (conda, pip, source): source

dask/array/tests/test_array_core.py::test_concatenate_flatten
dask/array/tests/test_array_core.py::test_normalize_chunks_nan dask/array/tests/test_array_core.py::test_stack_scalars dask/array/tests/test_array_core.py::test_astype dask/array/tests/test_array_core.py::test_meta[dtype1] dask/array/tests/test_array_core.py::test_vindex_basic dask/array/tests/test_array_core.py::test_from_array_with_missing_chunks dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index11-value11] dask/array/tests/test_array_core.py::test_reshape[original_shape15-new_shape15-2] dask/array/tests/test_array_core.py::test_from_array_scalar[int32] dask/array/tests/test_array_core.py::test_setitem_extended_API_2d[index18-value18] dask/array/tests/test_array_core.py::test_elemwise_uneven_chunks dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape3-v_shape3] dask/array/tests/test_array_core.py::test_to_hdf5 dask/array/tests/test_array_core.py::test_matmul dask/array/tests/test_array_core.py::test_map_blocks_block_info_with_new_axis dask/array/tests/test_array_core.py::test_to_delayed_optimize_graph dask/array/tests/test_array_core.py::test_concatenate_axes dask/array/tests/test_array_core.py::test_broadcast_to_scalar dask/array/tests/test_array_core.py::test_reshape[original_shape31-new_shape31-chunks31] dask/array/tests/test_array_core.py::test_Array_computation dask/array/tests/test_array_core.py::test_store_deterministic_keys[True-False] dask/array/tests/test_array_core.py::test_compute_chunk_sizes_warning_fixes_to_zarr dask/array/tests/test_array_core.py::test_normalize_chunks_tuples_of_tuples dask/array/tests/test_array_core.py::test_broadcast_operator[u_shape4-v_shape4] dask/array/tests/test_array_core.py::test_no_chunks_yes_chunks dask/array/tests/test_array_core.py::test_map_blocks_block_info dask/array/tests/test_array_core.py::test_asanyarray dask/array/tests/test_array_core.py::test_broadcast_to_chunks dask/array/tests/test_array_core.py::test_block_simple_column_wise 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